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Full text of "Effects of bubble coalescence and heater length scale on nucleate pool boiling"

- 1C->/M Corton r\^^^ 



EFFECTS OF BUBBLE COALESCENCE AND HEATER LENGTH SCALE ON 

NUCLEATE POOL BOILING 



uJl 



08Yr 



'"^~M 



By 

TAILIAN CHEN 



A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT 

OF THE REQUIREMENTS FOR THE DEGREE OF 

DOCTOR OF PHILOSOPHY 

UNIVERSITY OF FLORIDA 



2002 



^^::. 



ACKNOWLEDGMENTS 

I would like to express my sincere appreciation to my advisor, Dr. Jacob N. 
Chung, for his invaluable support and encouragement. Without his direction and support, 
this work would not have been possible. Many thanks go to Dr. Jungho Kim for his help 
build up the experimental setup and instructions in this research. I also greatly 
acknowledge Dr. James F. Klausner for his invaluable suggestions in this research. 

I have also had the privilege to work with Drs. William E. Lear, Jr., Zhuomin 
Zhang and Ulrich H. Kurzweg as other members of my committee. Their suggestions and 
encouragement have shaped this work considerably. 

Finally, I feel indebted to my wife, Lu Miao, and my son, Matthew Chen. Without 
their continuous support, this work would not have been possible. 



u 



TABLE OF CONTENTS 

page 

ACKNOWLEDGMENTS ii 

LIST OF TABLES vi 

LIST OF FIGURES vii 

NOMENCLATURE xi 

ABSTRACT xiv 

CHAPTER 

1 INTRODUCTION 1 

1.1 Statement of the Problem 1 

1.2 Research Objectives 2 

1.3 Significance and Justification 3 

2 LITERATURE REVIEW AND BACKGROUND 5 

2.1 Bubble Dynamics and Nucleate Boiling 5 

2.2 Coalescence of Bubbles 15 

2.3 Critical Heat Flux 21 

3 EXPERIMENT SYSTEM 24 

3.1 Microheaters and Heater Array 24 

3.1.1 Heater Construction 24 

3.1.2 Heater Specifications 25 

3.2 Constant Temperature Control and Data Acquisition System 27 

3.2.1 Feedback Electronics Loop 27 

3.2.2 ^Processor Control Board and D/A Board 28 

3.2.3 A/D Data Acquisition Boards 29 

3.2.4 Heater Interface Board (Decoder Board) 29 

3.2.5 Software 29 

3.3 Boiling Conditioin and Apparatus 30 

3.3.1 Boiling Condition 30 

3.3.2 Boiling Apparatus 30 



ui 



3.4 Experiment Procedure 30 

3.4.1 Heater Calibration 30 

3.4.2 Data Acquisition and Visualization 36 

3.5 Heat Transfer Analysis and Data Reduction 37 

3.5.1 Qualitative Heat Transfer Analysis 37 

3.5.2 Data Reduction Procedure 38 

3.5.3 Determination of Natural Convection on the Microheaters 40 

3.5.4 Uncertainty Analysis 44 

4 SINGLE BUBBLE BOILING EXPERIMENT 52 

4.1 Introduction 52 

4.2 Experiment Results 54 

4.2.1 Time-averaged Boiling Curve 54 

4.2.2 Time-resolved Heat Flux 55 

4.2.3 Time-resolved Heat Flux vs. Superheat AT 58 

4.2.4 Visualization Results and Bubble Growth Rate 63 

4.3 Comparison and Discussion 67 

4.3.1 Bubble Departure Diameter 67 

4.3.2 Size Effects on Boiling Curve and Peak Heat Hux 68 

4.3.3 Bubble Incipient Temperature 72 

4.3.4 Peak Heat Flux on the Microheater 72 

4.4 Deviations from Steady Single Bubble Formation 73 

4.4.1 Discontinued Bubble Formation 73 

4.4.2 Bubble Jetting 79 

5 DUAL BUBBLE COALESCENCE 86 

5.1 Synchronized Bubble Coalescence 86 

5.2 Dual Bubble Coalescence and Analysis 87 

5.3 Heat Transfer Enhancement due to Coalescence 93 

5.4 Bubble Departure Frequency 95 

6 HEAT TRANSFER EFFECTS OF COALESCENCE OF BUBBLES FROM 

VARIOUS SITE DISTRIBUTIONS 96 

6.1 Coalescence of Dual Bubbles with a Moderate Separate Distance - A Typical Case 

96 

6.2 Dual Bubble Coalescence from Heaters #1 1 and #14 at 100°C - Larger Separation 

Distance Case 103 

6.3 Dual Bubble Coalescence from Heaters #1 1 and #14 at 130°C - Larger separation 

Distance and Higher Heater Temperature Case 107 

6.4 History of Time-resolved Heat Flux for Different Heater Separations 109 

6.5 Time Period of a Bubbling Cycle 109 

6.6 Average Heat Flux of a Heater Pair - Effects of Separation Distance 1 13 

6.7 Time-averaged Heat Flux from Heater #1 1 13 

6.8 Coalescence of Multiple Bubbles 115 



IV 



6.9 Heat Transfer Enhancement due to Coalescence Induced Rewetting 122 

7 MECHANISTIC MODEL FOR BUBBLE DEPARTURE AND BUBBLE 

COALESCENCE 126 

7.1 Rewetting Model 127 

7.2 Results from the Rewetting Model 128 

8 CONCLUSIONS AND FUTURE WORK 132 

8.1 Summary and Conclusions 132 

8.2 Future Work 133 

APPENDIX NOTES OF PROGRAMMING CODES FOR DATA ACQUISITION.. 135 

REFERENCES 146 

BIOGRAPHICAL SKETCH 150 



LIST OF TABLES 

Tables Page 

3.1 The specifications of the D/A cards 29 

3.2 The uncertainty sources from calibration 46 

4.1 Single bubble growth time and departure diameter 68 

4.2 Properties of FC-72 at 56°C 68 

7.1 Effective thermal conductivity (w/m-K) used in the rewetting model 129 






'^. 



■^- r r 



^^ 






VI 



'j'^. ,'^: C*'^ ' v>i. 



T 



. f 4- .. » 

LIST OF FIGURES 



^■i 



Figures Page 

2.1 The numerical model and results given by Mei et al. (1995) 7 

2.2 The numerical model and four growth domains by Robinson and Judd (2001) 8 

2.3 Research on bubble coalescence by Li (1996) 17 

2.4 The coalescence research performed by Bonjour et al. (2000) 20 

3.1 Heaters and heater array 26 

3.2 Wheatstone bridge with feedback loop 28 

3.3 Boiling apparatus 31 

3.4 Schematic of calibration apparatus and temperature control loop 32 

3.5 Part of the calibration results 34 

3.6 Comparison of calibrated resistances of heater #1 with the calculated resistances 

from property relation 35 

3.7 The schematic showing the heat dissipation from a heater 39 

3.8 Heat flux comparison from experimental and calculated results 41 

3.9 Derived natural convection heat fluxes for different heater configurations 44 

3.10 The circuit schematic for temperature control and voltage division 47 

3.11 The uncertainty at different temperatures 50 

4.1 The boiling curve of the single bubble boiling 56 

4.2 The heat flux variation during one bubble cycle 57 

4.3 Time-resolved heat flux variation at different heater superheats 59 



'va 



4.4 The trend of maximum and minimum heat fluxes during one bubble cycle with 

various heater superheats 61 

4.5 A hypothetical model for bubble departure from a high temperature heater 62 

4.6 Bubble images of a typical bubble cycle taken from the bottom 64 

4.7 Measured bubble diameters at different time 66 

4.8 Bubble growth rate at different time 66 

4.9 The visualization result of bubble departure-nucleation process for heater #1 at 54°C 

69 

4.10 The relationship between bubble departure diameter and growth time 70 

4.11 Comparison of boiling curves 71 

4.12 Comparison of peak heat fluxes 71 

4. 13 The process of vapor explosion together with onset of boiling 75 

4.14 The ruler measuring the distance in figure 4.13 after vapor explosion 75 

4.15 The bottom images for vapor explosion and boiling onset process 76 

4.16 The heat flux variation corresponding to the vapor-explosion and boiling onset 

process 78 

4.17 The chaotic bubble jetting process for heater #1 at 110°C 81 

4.18 The bottom images of chaotic bubble jetting process for heater #1 at 1 10°C 82 

4.19 The heat flux traces corresponding to the bubble jetting process 83 

4.20 The heat flux traces for bubble jetting process from heater #1 at 105°C 84 

4.21 The heat flux traces for bubble jetting process from heater #1 at 120°C 85 

5.1 The heat flux variation for pair #1 with #11 and pair #1 and #12 88 

5.2 The heat flux variation of one typical bubble cycle for two configurations (a) and (b) 

for heater #1 with #11, (c) and (d) for heater #1 with #12 89 

5.3 The heater dry area before and after coalescence 90 



vm 



*. -J ... 

5.4 The boiling heat flux for the two pairs (#1 with #11) and (#1 with #12) as they are set 

at different temperatures to generate bubbles and coalesce 92 

5.5 The heat flux increase due to coalescence 94 

5.6 Comparison of bubble departure frequency from heater #1 for coalescence and non- 

coalescence cases 95 

6.1 The departing and nucleation process for heaters #1 1 and #13 at 100°C 99 

6.2 The coalescence process (2 cycles of oscillation) for heaters #1 1 and #13 at 100°C. 

100 

6.3 The heat flux history for dual bubble coalescence 101 

6.4 Photographs showing the interface interaction 102 

6.5 The side-view photographs of coalescence-departure-nucleation process for heaters 

#11 and #14 at 100°C 104 

6.6 The bottom view of coalescence-departure-nucleation process for heaters #11 with 

#14atl00°C 105 

6.7 The heat flux history from heater #1 1 when #1 1 and #14 are set at 100°C 106 

6.8 The heat flux history for heaters #1 1 and #14 at 130°C 108 

6.9 The heat flux history from heater #1 with time 1 10 

6.10 The bottom images for one bubble cycle and dryout changing (time in second) ... 1 1 1 

6.11 The time duration of one bubble cycle at different superheats 112 

6.12 The average heat fluxes from different pairs of heaters at different superheats 114 

6.13 The average heat fluxes from heater #1 at different superheats 1 14 

6.14 Four heater configurations for multiple bubble coalescence experiment 1 15 

6.15 The heat fluxes from each heater for case A (figure 6.14) vs. superheat 117 

6.16 The heat fluxes from each heater for case C (flgure 6.14) vs. superheat 1 17 

6.17 The average heat fluxes for different heater configurations vs. superheat 118 

6.18 The coalescence sequence for heaters #3, #5, #7, and #15 at 80°C 120 

'■ t 



6.19 The coalescence sequence for heaters #1, #3, #5, #7, and #15 at 80°C 120 

6.20 The coalesced bubble formed on heaters #3, #5, #7, and #15 at 100°C 121 

6.21 The coalesced bubble formed on heaters #1, #3, #5, #7, and #15 at 100°C 121 

6.22 The heat fluxes from heater #11 when the other heaters are at various superheats. 123 

6.23 The heat flux history from heater #1 1 during 0.8 second 123 

6.24 The heat flux history from heater #11 when the bubble formed on it is pulled 

toward the primary bubble from heaters #1, #2, #3, and #4 124 

7.1 Typical heat flux spikes during bubble coalescence 126 

7.2 The fluid flow induced by the bubble departure 127 

7.3 The fluid flow induced by the bubble coalescence 128 

7.4 The results from the rewetting model for the bubble coalescence 130 

7.5 The results from the rewetting model for the bubble departure 131 

A.l The main interface to select heaters 135 

A.2 Heaters temperature form 137 

A. 3 The architecture for addressing the selected heaters 141 

A.4 The pins layout of the D/A cards 143 

A. 5 The data acquisition form 144 



c- -^^ 



NOMENCLATURE 



heater surface area (cm^) 



C platinum constant coefficient (Q/Q°C) 

Cp,i specific heat (kJ/kg-K) 

Db bubble departure diameter 

D\ dimensionless bubble departure diameter 

Fo Fourier number 

g gravitational acceleration (m/s^) 

g(Pr) function of Prandtl number in Eq.(3.8) 

Gr^ Grashof number defined in Eq.(3.7) 

Hfg latent heat of vaporization (kJ/kg) 

Ja Jacob number 

k thermal conductivity (w/m-K) 

ktff effective thermal conductivity (w/m-K) 

L heater characteristic length 

Lo heater characteristic length 

n constant '■■ fr i, 

Nux Nusselt number 

Nu, average Nusselt number for a heater 



XI 



Lxdge 


corrected Nusselt number for a heater 


Pm 


hydrodynamic pressure 


Py 


vapor pressure inside a bubble 


Poo 


bulk liquid pressure - ^ 


Pn 


Prandtl number 


q" 


heat flux (w/cm^) 


It 

y condl 


conductive heat transfer rate per unit area from a heater to substrate with 
boiling (w/cm^) 


9"cond2 


conductive heat transfer rate per unit area from a heater to substrate 
without boiling (w/cm^) 


It 
H natural 


natural convection heat transfer rate per unit area from a heater (w/cm^) 


^"radl 


radiation heat transfer rate per unit area from a heater with boiling (w/cm^) 


^"rad2 


radiation heat transfer rate per unit area from a heater without boiling 
(w/cm^) 


y rawl 


total heat transfer rate per unit area supplied to a heater with boiling 
(w/cm^) 


^"raw2 


total heat transfer rate per unit area supplied to a heater without boiling 
(w/cm^) 


^"s(t) 


heat transfer with time in the rewetting model(w/cm^) 


9 "top 


boiling heat transfer (w/cm^) 


/J 


electrical resistance at temperature T 


/fb 


bubble diameter (mm) 


/fo 


resistance at ambient temperature To 


t - 


time (seconds) 


r, 


bulk liquid temperature (°C) 


n 


heater surface temperature (°C) 




jdi 



To ambient temperature (°C) 

V voltage across the heater (V) 
Voff offset voltage of the Opamp (V) 

Greek Symbols 

e uncertainty associated with temperature (°C) 

w uncertainty associated with heat flux (w/cm^) 

Pi liquid density (kgW) 

Pv vapor density (kg/m^) 

OCi thermal diffusivity (kJ/kg-K) 

T*g dimensionless bubble growth time 

Tg bubble growth time (seconds) 

fi coefficient of thermal expansion 

V kinematic viscosity (m/s^) 
jUi liquid viscosity (NsW) 
CT surface tension (N/m) 
ATe. heater superheat (°C) 



xiu 



Abstract of Dissertation Presented to the Graduate School 

of the University of Florida in Partial Fulfillment of the 

Requirements for the Degree of Doctor of Philosophy 

EFFECTS OF BUBBLE COALESCENCE AND HEATER LENGTH SCALE ON 

NUCLEATE POOL BOILING 

By 

Tailian Chen 
. August 2002 

Chairman: Jacob N. Chung 

Major Department: Mechanical Engineering 

Nucleate boiling is one of the most efficient heat transfer mechanisms on earth. 
For engineering applications, nucleate boiling is the mode of choice owing to its narrow 
operating temperature range and high heat transfer coefficient. Though much effort has 
been expended in numerous investigations over several decades, controversies persist, 
and a complete understanding of the boiling mechanisms still remains elusive. 

In this research, microscale array heaters have been utilized, where each heater 
has a size of 270 jim x 270 ^im. The time and space-resolved heat fluxes from constant- 
temperature heaters were acquired through a data acquisition system with side and 
bottom images taken from the high speed digital visualization system. Together with the 
heat fluxes from the heaters, we have been able to obtain much better new results. 

For the single bubble boiling, we found that in the low superheat condition, 
microlayer evaporation is the dominant heat transfer mechanism while in the high 



XIV 



superheat condition, conduction through a vapor film is dominant. During the bubble 
departure, a heat flux spike was measured in the lower superheat regime whereas a heat 
flux dip was found in the higher superheat regime. As the heater size is reduced in pool 
boiling, the boiling curve shifts towards higher fluxes with corresponding increases in 
superheats. Comparing with the single bubble boiling, two major heat flux spikes have 
been recorded in dual bubble coalescence. One is due to the bubble departure from the 
heater surface and the other one is due to the bubble coalescence. The overall heat 
transfer is increased due to the rewetting of the heater surface as a result of bubble-bubble 
interaction. A typical ebullition cycle includes nucleation, single bubble growth, bubble 
coalescence, continued bubble growth and departure. We have found that in general the 
coalescence enhances heat transfer as a result of creating rewetting of the heater surface 
by colder liquid and turbulent mixing effects. The enhancement is proportional to the 
ebullition cycle frequency and heater superheat. It was also measured that the longer the 
heater separation distance is the higher the heat transfer rate is from the heaters. For the 
multiple bubble coalescence, the key discovery is that the ultimate bubble that departs the 
heater surface is the product of a sequence of coalescence by dual bubbles. For the heat 
transfer enhancement, it was determined that the time and space averaged heat flux for a 
given set of heaters increases with the number of bubbles involved and also with the 
separation distances among the heaters. In particular, we found that the heat flux levels 
for the internal heaters are relatively lower than those of the surrounding ones. 



*A 



■■ '^ ■: i * t' 



.,v ^ 



< ,'■'■ ■>■■ 

70/ 






CHAPTER 1 
INTRODUCTION 

1.1 Statement of the Problem 

In nucleate boiling from a heated surface, vapor bubbles generated tend to interact 
with neighboring bubbles when the superheat is high enough to activate higher nucleation 
site density. It is believed that bubble-bubble interaction and coalescence are responsible 
mechanisms for achieving high heat transfer rates in heterogeneous nucleate boiling. 
Bubble-bubble coalescence creates strong disturbances to the fluid mechanics and heat 
transfer of the micro- and macro-layer beneath the bubbles. Because of the complicated 
nature, the detailed physics and the effects of the bubble-bubble interaction process have 
never been completely unveiled. 

During the terrestrial pool boiling, the critical heat flux (CHF), which is the upper 
heat transfer limit in the nucleate boiling, represents a state of balance. Because the 
buoyancy force strength is relatively constant on earth, for heat fluxes lower than the 
CHF, this force is more than that required for a complete removal of vapor bubbles 
formed on the heater surface. At the CHF, the buoyancy force is exactly equal to the 
force required for a total removal of the vapor bubbles. For heat fluxes greater than the 
CHF, the buoyancy force is unable to remove all the bubbles, thus resulting in the 
accumulation and merging of bubbles on the heater surface, which eventually leads to a 
total blanketing of the heater surface by a layer of superheated vapor. Heat transfer 
through the vapor film, so-called film boiling, is much less efficient than the nucleate 
boiling and produces very high heater surface temperatures. 

r ■ . - -...• . --. *..•• j 



In many modem heat transfer applications, the length scale of heat source gets 
smaller, where traditional boiling theory may not be applicable. How does the length 
scale affect the boiling phenomenon? How do we maximize the heat transfer from a 
limited heater surface? Those are frequent questions asked by industrial engineers. There 
is no way to accurately answer these questions without the knowledge of microscale 
boiling phenomenon. 

1.2 Research Objectives 

This research seeks to perform high-quality experiments to unmask the effects of 
bubble coalescence and length scale of heaters on heterogeneous nucleate boiling 
mechanisms. Through this research, we would be able to achieve the following: 

1. To find the basic physics of bubble coalescence and its effects on fluid 
mechanics and heat transfer in the micro- and macro-layers and to develop a simple 
mechanistic model for this phenomenon. 

2. To obtain a fundamental understanding of the effects of heater length scale on 
the boiling mechanism and boiling heat transfer. 

' We intend to study the detailed physics of bubble formation on small heaters, 
bubble coalescence and bubble dynamics, and heat and mass transport during bubble 
coalescence. The purpose is to delineate through experiment and analysis the 
contributions of the key mechanisms to total heat transfer. This includes micro/macro 
layer evaporation on single and merged bubbles attached to a heated wall, and heat 
transfer enhancement during coalescence of bubbles on the heater wall. We intend to 
provide answers to the following: 

How will the bubble coalescence affect the heat transfer from the heater surface? 



What mechanisms are at play during bubble coalescence? In other words, how do 
the thermodynamic force, surface tension force, and hydrodynamic force that are 
associated with the merging process balance one another? 

What controls the bubble nucleation, growth, and departure from the heater 
surface in nucleate boiling when bubble coalescence is part of the process? 

How does the heater surface superheating level affect the bubble coalescence? 

How does the heater length scale affect the bubble inception and boiling heat 
transfer? 

1.3 Signiflcance and Justiflcation 

Nucleate boiling has been recognized as one of the most efficient heat transfer 
mechanisms. In many engineering applications, nucleate boiling heat transfer is the mode 
of choice. BoiUng heat transfer has the potential advantage of being able to transfer a 
large amount of energy over a relatively narrow temperature range with a small weight to 
power ratio. For example, boiling heat transfer has been widely used in microelectronics 
cooling. 

Apart from the engineering importance, there are science issues. Currently, the 
mystery of critical heat flux remains unsolved. As a matter of fact controversies over the 
basic transport mechanisms of bubble coalescence and its effects on the role of 
microlayer and macrolayer, liquid resupply and heater surface property continue to 
puzzle the heat transfer community. With the micro-array heaters, high speed data 
acquisition system and high speed digital camera, we would have a better chance to 
unlock the secrets of nucleate boiling. Boiling is also an extremely complex and elusive 
process. Although a very large number of investigators have worked on boiling heat 
transfer during the last half century, unfortunately, for a variety of reasons, far fewer 
efforts have focused on the physics of boiling process. Most of the reported work has 
been tailored to meeting the needs of engineering applications and as a result has led to 



correlations involving several adjustable parameters. The correlations provide a quick 
input to design, performance and safety issues; hence they are attractive on a short-term 
basis. However, the usefulness of the correlations diminishes very rapidly as parameters 
of interest start to lie outside the range for which the correlations were developed. 






CHAPTER 2 
LITERATURE REVIEW AND BACKGROUND 

2.1 Bubble Dynamics and Nucleate Boiling 

Boiling is an effective heat transfer mode because a large amount of heat can be 
removed from a surface with a relatively small temperature difference between the 
surface and the bulk liquid. Boiling bubbles have been successfully applied in ink-jet 
printers and microbubble-powered acuators. The technologies still in the research and 
development stage for possible applications include TIJ printers, optical cross-connect 
(OXC) switch, micropumping in micro channels, fluid mixers for chemical analysis, fuel 
mixers in combustion, prime movers in micro stem engines, and the heat pumps for 
cooling of semiconductor chips in electronic devices. The boiling curve first predicted by 
Nukiyama (1934) has been used to describe the different regimes of saturated pool 
boiling. But until now, there are no theories or literature that exactly explains the 
underlying heat transfer mechanisms. Forster and Grief (1959) assumed that bubbles act 
as micropumping devices removing hot fluid from the wall, replacing it with cold liquid 
from the bulk. The proposed equation for calculating the boiling heat transfer is 



^ = A^p/ 



V 3 ; 



rL 



(T -T, \ 



-t; 



/ ,- (2.1) 



2 

Mikic and Rohsenow (1969) developed a model whereby the departing bubble 
scavenges away the superheated layer, initiating transient conduction into the liquid. 
They also proposed the heat flux calculation by the expression 






_1 .. ^ ■ 



q"- 



fAkp,c \"' 



"i^pi 



n 



[T.-T.,.]f"' (2.2) 



Mei et al. (1994) investigated the bubble formation and growth by considering 
simultaneous energy transfer among the vapor bubbles, liquid microlayer, and the heater. 
They presented the sketch for a growing bubble, microlayer and heating solid which is 
shown in figure 2.1(a), where the bubble dome has the shape of a sphere of radius of 
Rbit), the microlayer has a wedge shape with a radius Rb(t), wedge angle (p centered at r 
= 0. 

They found that four dimensionless parameters governing the bubble growth rate 
are Jacob number, Fourier number, thermal conductivity and diffusivity ratios of liquid 
and solid. And the Jacob number is the most important one affecting c and ci, two 
empirically determined constants that depict the bubble shape and microlayer wedge 
angle. Using this model, they examined the effects of varying Ja, Fo, k, a\ separately. 
The results are shown in figure 2.1(b), and they claim that the effects of 7^, Fo, k, Oi on 
the normalized growth rate /?b(0 are the following: (1) increasing Ja and «] will result in 
an increasing Rb(t), and (2) increasing Fo and k will result in a decreasing Kbit). 

Recently, Robinson and Judd (2001) developed a theory to manifest the 
complicated thermal and hydrodynamic interactions among the vapor, liquid and solid for 
a single isolated bubble growing on a heated plane surface from inception. They use the 
model shown in figure 2.2(a) to investigate the growth characteristics of a single isolated 
hemispherical bubble growing on a plane heated surface with a negligible effect of an 
evaporating microlayer. They demarcate the bubble growth into four regions, surface 
tension controlled growth (ST), transition domain (T), inertial controlled growth (IC), and 






liquid niiorolajrcr 




t»H 



(a) 




1.0 



0.8 



o.e 



0.4 - 



0.0 



1 1 


— 1 1 — r 

r»-o.oi 
1 


- 






y;!!^^''''^ 100 


y^^ 


.^.- "^ 1000 


1 1 


■ 10000- 

1 1 1 



0.0 0.2 0.4 0.6 0.8 1.0 1.3 

T 



1.2 
1.0 
0.8 

0.4 

0.2 



0.0 



-i r 


— 1 1 r-' 

«. 0006. 


- 


^^</^<x» - 


-./ 


0.01 




05 _ 
1 1 1 



0.0 0.2 0.4 0.6 0.8 1.0 1.2 



(•) 




Parametric dependence of the nonnalized growth rate H(x\. (a) /a - I. 10, 100 and 1000 at (Fo, K. 
a) . (1, 0.005, 0.005); (b) fo -0.01, I, 10. 100, 1000 and 10000 at (Ja. k, a) - (10. 0.005. 0.005); (c) 
K - 0.0005, 0.001. 0.01, 0.05 a( {Ja. Fo. i) •= (10, 1. 0.005) and (d) » - 0.0005, 0.001. 0.01 and 0.05 at (Ja. . 

Fo.K)- (10, 1,0.005). 



(b) 



Figure 2.1 The numerical mocJel and results given by Mei et al. (1995). (a) The numerical 

model; (b) The numerical results. 




liquid, P. , T. 



(f b, Zb) 



qw" 



PUne Heated Surface 



r 



(a) 



200 
180 
160 
-5- 140 
I. 120 
100 



80 

1 60 
40 
20 


-20 
-40 



; (a) 

3. 
2- 


T 


1 

1 2 
3 


p,-p. 
p.. 

R 




: ST 


IC 


1 


HT 



0.10 



0.05 



0,00 



-0.05 




100 



0.000001 0.0001 0.01 1 

Time (ms) 



100 



(b) 

Figure 2.2 The numerical model and four growth domains by Robinson and Judd (2001). 

(a) The numerical model-Hemispherical bubble growing on a plane heated surface; (b) 

The four growth domains with continent pressures at each domain. 



9 

heat transfer controlled growth (HT), which are shown in figure 2.2(b). During the 
surface-controlled domain, they claim that energy is continuously transferred into the 
bubble by conduction through liquid. But the average heat flux, thus the growth rate 
d/?b/df, is so small that the contribution of the hydrodynamic pressure in balancing the 
equation of motion is insignificant so that it essentially reduces to a static force balance, 
Py - P^ = 2(j/Rb, as shown in figure 2.2(b). The bubble growth in this domain is 
accelerated due to a positive feedback effect in which the increase in the radius, R^, is 
related to a decreasing interfacial liquid temperature. This corresponds to an increase in 
q", through the increase in the magnitude of the local temperature gradient, which feeds 
back by a proportional increase in the bubble growth rate dRb/dt. In the earliest stage of 
the surface tension domain, this feedback is not significant. However, in the latter stage, 
it becomes appreciable as indicated by a noticeable increase in /?b away from /?bc, a 
significant decrease in both Tv and Pv and a sharp increase in q". At the transition 
domain, the hydrodynamic force P^ rises sharply due to the significant liquid motion 
outside of the bubble interface. Though q" and dRb/dt increase at the beginning of this 
stage, they are shown to decrease in the latter stage and reach the maximum value. One of 
the reasons for this decrease in spite of a positive feedback of surface-controlled growth 
can be additional resistance associated with forcing the bulk liquid out radially. The other 
reasons can be due to the conduction and advection occurring in the liquid adjacent to the 
interface. Each of these heat transfer mechanisms acts in such a way as to diminish the 
temperature gradients in the immediate vicinity of the vapor-liquid interface and thus has 
a detrimental influence on the rate at which q" and dR^/dt increase. The inertial controlled 
growth refers to the interval of bubble growth in which the rate of bubble expansion is 
considered to be limited by the rate at which the growing interface can push back the 



10 

surrounding liquid (Carey, 1992). In this domain, the average heat flux into the bubble is 
very high, so heat transfer to the interface is not the limiting mechanism of the growth. 
The pressure difference, Pv - Po., is now balanced by the hydrodynamic pressure at the 
interface. The hydrodynamic pressure comprises two "inertial" terms, i.e., the 
acceleration term, pi/?b(d^/?b/dt^), and the velocity term, 3/2pi(dRb/dtf. The two terms are 
of differing signs and thus tend to have an opposite influence on the total liquid pressure, 
and thus the force of the liquid on the bubble interface. This inertial controlled growth 
domain is characterized by a decreasing average heat flux and a decelerating interface. 
This signifies that the positive influence that the decreasing vapor temperature tends to 
have on the local temperature gradient is not sufficient to compensate for the rate at 
which advection and conduction serve to decrease the temperature gradient at the 
interface. The heat transfer controlled growth domain refers to the interval of bubble 
expansion and is considered to be limited by the rate at which liquid is evaporated into 
the bubble, which is dictated by the rate of heat transfer by conduction through the liquid 
(Carey, 1992). In this latter stage of bubble growth, the interface velocity has slowed 
enough so that the hydrodynamic pressure, P^, becomes insignificant compared with the 
surface tension term, 2a//?b, in balancing the pressure difference, Pv - P^. This is shown 
in figure 2.2(b). Because the liquid temperature at the interface is now constant, the 
positive feedback effect, responsible for the rapid acceleration of the vapor-liquid 
interface in the surface tension controlled region, does not occur in this domain of 
growth. Conversely, the "shrinking" and "stretching" of the thermal layer in the liquid 
due to conduction and advection are responsible for the continuous deceleration of the 
interface due to the diminishing interfacial temperature gradients. 



11 

The steady cyclic growth and release of vapor bubbles at an active nucleation site 
are termed an ebullition cycle. This bubble growth process begins immediately after the 
departure of a bubble. Bulk fluid replaces the vapor bubble initially. A period of time, 
called waiting period, then elapses during which transient conduction into the liquid 
occurs but no bubble growth takes place. After this, the bubble begins to grow as the 
thermal energy needed to vaporize the liquid at the interface arrives. This energy comes 
from the liquid region adjacent to the bubble that is superheated during the waiting period 
and from the heated surface. As the bubble emerges from the site, the liquid adjacent to 
the interface is highly superheated and the transfer of heat is not a limiting factor. 
However, the resulting rapid growth of the bubble is resisted by the inertia of the liquid 
and, therefore, the bubble growth is considered to be inertia controlled. During the 
inertia-controlled growth, the bubble generally grows radially in a hemispherical shape. 
A thin microlayer (evaporation microlayer) is formed between the lower portion of the 
bubble interface at the heated wall. Heat is said to transfer across the thin film from the 
wall to the interface by directly vaporizing liquid at the interface. The liquid region 
adjacent to the bubble interface (relaxation microlayer) is gradually depleted of its 
superheat as the bubble grows. Therefore, as growth continues, the heat transfer to the 
interface may become the limiting factor and the bubble is said to be heat transfer 
controlled. It is easy to see that vapor bubbles grow in two distinct stages. Fast growth 
emerges initially, followed by a slow growth period until detachment. 

In general, very rapid, inertia controlled growth is more likely under the following 
conditions which typically produce a build-up of high superheat levels during the waiting 
period and/or cause rapid volumetric growth (Carey, 1992). 

- High wall superheat 



12 

- High imposed heat flux 

- Highly polished surface having only very small cavities 

- Very low contact angle (highly wetting liquid) 

- Low latent heat of vaporization 

- Low system pressure (resulting in low vapor density) 

Heat transfer controlled growth of a bubble is more likely for conditions which 
result in slower bubble growth or result in a stronger dependence of bubble growth rate 
on heat transfer to the interface. They include: 

- Low wall superheat 

- Low imposed heat flux 

- A rough surface having many large and moderately sized cavities 

- Moderate contact angle and moderately wetting liquid 

- High latent heat of vaporization 

- Moderate to high system pressures 

The forces acting on a bubble can be a very complicated issue. It is highly 
dependent on the bubble stages during its cyclic process. Among all forces, dominant 
force can vary depending on the bubble stages, surface superheat, boiling condition, and 
so forth. In general, the following major forces can be involved during boiling: surface 
tension, buoyancy force, inertia of induced liquid flow, drag force, internal pressure, 
adhesion force from the substrate, etc. In a flow boiling field, due to possible bubble slide 
before the bubble lifts off, boiling becomes even more complicated. Klausner et al. 
(1993) have studied bubble departure on an upward facing horizontal surface using R-1 13 
as the test fluid. By balancing forces due to surface tension, quasi steady drag, liquid 
inertia force due to bubble growth, buoyancy, shear lift force, hydrodynamic pressure and 



13 

contact pressure along and normal to the heater surface, they found that the bubble will 
slide before lift-off. The predicted bubble diameter at the beginning of sliding motion was 
found to agree well with their data. It was noted that liquid inertia force resulting from 
the bubble growth played a more important role in holding the bubble adjacent to the 
heater surface than the surface tension. However, such a conclusion is highly dependent 
on the base diameter that is used in calculating the force due to surface tension. In a 
subsequent study, Zeng et al. (1993) correlated both bubble diameter at departure and the 
lift off diameter by assuming that the major axis of the bubble became normal to the 
surface after the bubble began to slide. By balancing the components of buoyancy, liquid 
inertia, and shear lift force in the direction of flow, they were able to predict bubble 
diameter at departure. The bubble lift-off diameter was determined by balancing forces 
due to buoyancy and liquid inertia associated with bubble growth. For the evaluation of 
liquid inertia, the proportionality constant and the exponent in the dependence of bubble 
diameter on time were obtained from the experiments. Mei et al. (1999) have included 
the surface tension force, liquid inertia, shear lift force and buoyancy to determine the 
bubble lift-off diameter. For the model the bubble lift off diameter was shown to decrease 
with flow velocity and slightly increase with wall superheat. Maity and Dhir (2001) 
experimentally investigated the bubble dynamics of a single bubble formed on a 
fabricated micro cavity at different orientations of the heater surface with respect to the 
horizontal surface. They found that under flow boiling conditions bubbles always slide 
before lift off and the bubble departure diameter depends solely on the flow velocity and 
is independent of the inclination of the surface. Bubble departure diameter decreases with 
the flow velocity. Bubble lift-off diameter depends on both the flow velocity and the 






14 

angular position. Lift-off diameter increases with the angular position but decreases with 
the flow velocity. , ., 

On the other hand, commercial success of bubble jet printers (Nielsen, 1985) has 

inspired many researchers to apply bubble formation mechanisms as the operation 

principle in microsystems. For this purpose, the bubble from a microheater should be 

designed to present a stable, controllable behavior. Therefore, it is important to 

understand the bubble formation mechanisms in microheaters before they may be 

optimally designed and operated. Some previous work has been done in investigating 

bubble formation mechanism. lida et al. (1994) used a 0.1mm x 0.25mm x 0.25nm film 

heater subjected to a rapid heating (maximum 93 x 10^ K/s). They measured the 

temperature of heaters by measuring the electrical resistance. The temperature measured 

at bubble nucleation suggested homogeneous bubble nucleation in their experiment. But 

the heater they used does not ensure a uniformly heated surface. Lin et al. (1998) used a 

line resistive heater 50 x 2 x 0.53 pim^ to produce microbubbles in Fluorinert fluids. By a 

computational model and experimental measurements, they concluded that homogeneous 

nucleation occurs on these micro line heaters. They also reported that strong Marangoni 

effects prevent thermal bubbles from departing. Avedisian et al. (1999) performed 

experiments on a heater (64.5^im x 64.5^m x 0.2|im) used on the commercial thermal 

Inkjet printer (TIJ) by applying voltage pulses with short duration. They claimed that 

homogeneous nucleation at a surface is the mechanism for bubble formation with an 

extremely high heating rate (2.5 x 10^ K/s), and this nucleation temperature increases as 

the heating rate increases. Zhao et al. (2000) used a thin-film microheater of size of 

lOO^m X llOjim to investigate the vapor explosion phenomenon. They placed the 

microheater underside of a layer of water (about 6|im), and the surface temperature of the 



15 

heater was rapidly raised electronically well above the boiling point of water. By 
measuring the acoustic emission from an expanding volume, the dynamic growth of the 
vapor microlayer is reconstructed where a linear expansion velocity up to 17 m/s was 
reached. Using the Rayleigh-Plesset equation, an absolute pressure inside the vapor 
volume of 7 bars was calculated from the data of the acoustic pressure measurement. In a 
heat transfer experiment, Hijikata et al. (1997) investigated the thermal characteristics 
using two heaters of 50[im x SO^im and 100|im x lOOjxm, respectively. They found that 
70-80% of heat generated was released through a phase change process and heat is 
initially conducted in the glass substrate, then, it is transferred to the liquid layer above 
the heater and finally released through the evaporating process. Most of these works are 
based on applying a constant current or voltage so that the heat flux on the heater is 
maintained constant. 

2.2 Coalescence of Bubbles 

The suggested theory about boiling mechanism is that as the temperature of a 
heater surface increases from the onset of nucleate boiling, more bubbles are nucleated 
and coalesce simultaneously on the heater surface, which makes the heat flux higher and 
higher until the critical heat flux point (CHF). It has been considered for a long time that 
bubble-bubble coalescence plays an important, if not dominant, role in the high heat flux 
nucleate boiling regime and during the CHF condition as well. Because of the 
microscopic nature and complicated flow and heat transfer mechanisms, the research on 
coalescence has not progressed very fast in both experimental and theoretical fronts. 
Coalescence of bubbles on a surface is a highly complicated process that is involved with 
a balance among surface tension, viscous force and inertia. The phenomenon is 



16 

intrinsically a fast transient event. For the above reasons, the research of coalescence 
between bubbles has been rather limited. 

Li (1996) claims when two small bubbles approach each other, a dimpled thin 
liquid film is formed between them, as shown in figure 2.3(a). He developed a model for 
the dynamics of the thinning film with mobile interfaces, in which the effects of mass 
transfer and physical properties upon the drainage and rupture of the dimpled liquid film 
are investigated. The model predicts the coalescence time, which is the time required for 
the thinning and rupture of the liquid film, given only the radii of the bubbles and the 
required physical properties of the liquid and the surface such as surface tension, London- 
van der Waals constants, bulk and surface diffusion coefficients. The comparison of the 
predicted time of coalescence and experimental results is shown in figure 2.3(b), which 
shows that predicted coalescence is less than experimental results, and much less than the 
results predicted when the immobile interface is considered. In his research, no heat 
transfer is considered to affect the bubble coalescence. 

Yang et al. (2000) performed a numerical study to investigate the characteristics 
of bubble growth, detachment and coalescence on vertical, horizontal, and inclined 
downward-facing surfaces. The FlowLab code, which is based on a lattice-Boltzmann 
model of two-phase flows, was employed. Macroscopic properties, such as surface 
tension and contact angle, were implemented through the fluid-fluid and fluid-sohd 
interaction potentials. The model predicted a linear relationship between the macroscopic 
properties of surface tension and contact angle, and microscopic parameters. 
Hydrodynamic aspects of bubble coalescence are investigated by simulating the growth 
and detachment behavior of multiple bubbles generated on horizontal, vertical, and 



17 




(a) 



BOO 



200 



immobile inttrfoce (a) 

pretent study 

ooooo txparimtntal 




0.00 



0.02 0.04 

RJ (em) 



0.06 



(b) 



Figure 2.3 Research on bubble coalescence by Li (1996). (a) The thin liquid film between 
bubbles; (b) Comparison of the predicted results with experimental results. 



l^ ■ , 



■P 



18 

inclined downward-facing surfaces. For the case of horizontal surface, three distinct 
regimes of bubble coalescence were represented in the lattice-Boltzmann simulation: 
lateral coalescence of bubbles situated on the surface; vertical coalescence of bubbles 
detached in a sequence from a site; and lateral coalescence of bubbles, detached from the 
surface. Multiple coalescence was predicted on the vertical surface as the bubble 
detached from a lower elevation merges with the bubble forming on a higher site. The 
bubble behavior on the inclined downward-facing surface was represented quite similarly 
to that in the nucleate boiling regime on a downward facing surface. 

Bonjour et al. (2000) performed an experimental study of the coalescence 
phenomenon during nucleate pool boiling. Their work deals with the study of the 
coalescence phenomenon (merging of two or more bubbles into a single larger one) 
during pool boiling on a duraluminium vertical heated wall. Various boiling curves 
characterizing boiling (with or without coalescence) from three artificial nucleation sites 
with variable distance apart are presented. The heat flux ranges from 100 to 900 w/cm^ 
and the wall superheat from 5 to 35 K. They pointed out that the coalescence of bubbles 
growing on three sites results in higher heat transfer coefficients than single-site boiling, 
which is attributed to the supplementary microlayer evaporation shown in figure 2.4(a). 
However, the highest heat transfer coefficients are obtained for an optimal distance 
between the sites for which coalescence does not occur. They used different inter-site 
distances (a = 0.26mm, 0.64nim, 1.05mm, 1.50mm, 1.82mm) to generate bubbles and 
stated that for low and high intersite distances, the heat flux deviation is limited by the 
seeding phenomenon and the intersite distance, respectively, whereas for moderate 
intersite distances, the heat flux deviation is maximum because of the vicinity of the sites 
and absence of seeding. They also showed that due to bubble coalescence there is a 



19 

noticeable change of the slope of the coiling curve. They claim that such a change is 
attributed to coalescence and not to the progressive activation of the sites. They also 
showed that the coalescence of two bubbles has a much lower effect on the slope of the 
boiling curve, because the supplementary microlayer evaporation with two bubbles is 
lower than with three bubbles and consequently has a lower effect on the heat transfer 
coefficient. They used the influence area shown in figure 2.4(b) to depict the locations of 
the influence areas for various intersite distances. For a = 0.26mm, the influence area is 
overlapped for the three bubbles, thus a small overall influence area, which for the heater 
of larger area results in a large heat transfer coefficient. They also proposed a map for 
activation and coalescence that is shown in figure 2.4(c). In their experiment, it is also 
shown that coalescence results in a decrease in the bubble frequency. 

Haddad and Cheung (2000) found that the coalescence of bubbles is one of the 
phases in a cyclic process during nucleate boiling on a downward-facing hemispherical 
surface. Bubble coalescence follows the phase of bubble nucleation and growth but 
precedes the large vapor mass ejection phase. A mechanistic model based on the bubble 
coalescence in the wall bubble layer was proposed by Kwon and Chang (1999) to predict 
the critical heat flux over a wide range of operating conditions for the subcooled and low 
quality flow boiling. Comparison between the predictions by their model and the 
experimental CHF data shows good agreement over a wide range of parameters. The 
model correctly accounts for the effects of flow variables such as pressure, mass flux and 
inlet subcooling in addition to geometry parameters. Ohnishi et al. (1999) investigated the 
mechanism of secondary bubble creation induced by bubble coalescence in a drop tower 
experiment. They also performed a two-dimensional numerical simulation study. They 



20 




-»vrft««i^B^EtSB>8:l»f:3!W»!aai 



(a) 




(b) 



so 


^ 


V ' -^ ■ ' ' ^ 


40 




\\ . 




/JlJ/I « \\ o " 






W 


/j^ \ \S^ 1 01 lion °o 


A 


yyy \ ^$s^ *'"~ 






!0 


; *. ^^^^^^^^^X"" 








A * ^^"'■^-^Ji^*'''^*"**— 


10 


o>»™ ' A °« 




°"™" I5n» 




. 



I 



'Haiv.ill.°3ialv. 



^. 



(C) 



Figure 2.4 The coalescence research performed by Bonjour et al. (2000). (a) The 
additional microlayer formed; (b) Schematic representation of influence-area; (c) 

Coalescence and activation map. 



21 

reported that the simulation results agree well with the experimental data and indicate 
that the size ratio and the non-dimensional surface tension play the most important role in 
the phenomenon. 

2.3 Critical Heat Flux 

The boiling curve was first identified by Nukiyama (1934) more than sixty years 
ago. Since then the critical heat flux (CHF) has been the focus of boiling heat transfer 
research. A plethora of empirical correlations for the CHF are now available in the 
literature, although each is applicable to somewhat narrow ranges of experimental 
conditions and fluids. Recently a series of review articles (Lienhard 1988a,b, Dhir, 1990, 
Katto, 1994, Sadasivan et al., 1995) have been devoted to the discussion of progress 
made in the CHF research. The consensus is that a satisfactory overall mechanistic 
description for the CHF in terrestrial gravity still remains elusive. The following are some 
perspectives on issues in CHF modeling elucidated in a recent authoritative review by 
Sadasivan et al. (1995). 

1. CHF is the limiting point of nucleate boiling and must be viewed as linked to 
high-heat-flux end of nucleate boiling region and not an independent pure hydrodynamic 
phenomenon. The experiments dealing with CHF will be meaningful if only 
measurements of the high heat-flux nucleate boiling region leading up to CHF are made 
together with the CHF measurement. This would help resolve the issue of the role of dry 
area formation and the second transition region on CHF. Simultaneous surface 
temperature measurements are necessary. 

2. Measurements of only averaged surface temperature in space or in time 
actually mask the dynamics of the phenomena. An improved mechanistic explanation of 
CHF also requires that experimental efforts be directed towards making high resolution 



22 

and high-frequency measurements of the heater surface temperature. Experiments 
designed to make transient local point measurements of surface temperature (temperature 
map) and near surface vapor content will help in developing a clearer picture of the 
characteristics of the macrolayer and elucidating the role of liquid supply to the heater 
surface. Microsensor technology appears to be one area that shows promise in this 
respect. 

3. Identifying the heater surface physical characteristics such as active nucleation 
site distribution, static versus dynamic contact angles, and advancing versus receding 
angles. These would help understand the heater surface rewetting behavior. 

Sakashita and Kumada (1993) proposed that the CHF is caused by the dryout of a 
liquid layer formed on a heating surface. They also suggested that a liquid macrolayer is 
formed due to the coalescence of bubbles for most boiling systems, and that the dryout of 
the macrolayer is controlled by the hydrodynamic behavior of coalesced bubbles on the 
macrolayer. Based on these considerations, a new CHF model is proposed for saturated 
pool boiling at higher pressures. In the model, they suggest that a liquid macrolayer is 
formed due to coalescence of the secondary bubbles formed from the primary bubbles. 
The detachment of the tertiary bubbles formed from the secondary bubbles determines 
the frequency of the liquid macrolayer formation. The CHF occurs when the macrolayer 
is dried out before the departure of the tertiary bubbles from the heating surface. One of 
the formulations of the model gives the well-known Kutateladze or Zuber correlation for 
CHF in saturated pool boiling. 

The vast majority of experimental work performed to date utilized the heat flux- 
controlled heater surface to generate bubbles. Rule and Kim (1999) were the first to 
utilize the micro heaters to obtain a constant temperature surface and produced spatially 

■'.:"■■ ..HO?'--' I- 



23 

and temporally resolved boiling heat transfer results. Bae et al. (1999) used identical 
micro heaters as those used by Rule and Kim (1999) to study single bubbles during 
nucleate boiling. They performed heat transfer measurement and visualization of bubble 
dynamics. In particular, it was found that a large amount of heat transfer was associated 
with bubble nucleation, shrinking of dry spot before departure, and merging of bubbles. 
In this research, identical micro heaters to those of Rule and Kim (1999) were used to 
investigate the boiling microscopic mechanisms through the study of single bubbles 
boiling and the coalescence of bubbles. For each experiment, the temperature of the 
heaters was kept constant while the time-resolved and space-resolved heat fluxes and 
bubble images were recorded. 






4 f'\'"'.rv 



i 

i 

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i 



O^'^ji: 



CHAPTER 3 
EXPERIMENT SYSTEM 

3.1 Microheaters and Heater Array 

3.1.1 Heater Construction 

This section describes briefly the heater array construction. The details can be 
referred to T. Rule, Design, Construction, and Qualification of a Microscale Heater 
Array for Use in Boiling Heat Transfer, Master of Science thesis in mechanical 
engineering at the Washington State University, 1997. 

The heater array is constructed, as shown in figure 3.1(a), by depositing and 
etching away layers of conductive and insulating material on a quartz substrate to form 
conductive paths on the surface which will dissipate heat when electrical current is 
passed through them. The basic element of the microscale heater array is the serpentine 
platinum heater. The heater element, as shown in figure 3.1(b), is constructed by 
depositing platinum onto the substrate surface, masking off the heater lines, and etching 
platinum away from the unmasked areas. The terminal ends of each platinum heater are 
connected to the edge of the chip with aluminum leads deposited on the chip. Substrate 
conduction was reduced by using a quartz (^ = 1.5 w/mK) substrate instead of a silicon {k 
= 135 w/mK) substrate, since silicon is 90 times more thermally conductive than quartz. 
A Kapton {k = 0.2 w/mK) would further reduce substrate conduction, but it has not yet 
been tested as a substrate material. Quartz is an electrical insulator, so the substrate 
cannot be used as an electrical ground, as it was when silicon was used. An aluminum 
layer was deposited over the platinum heaters to serve as a common heater ground. 



24 



25 

Something must be used to separate the platinum heaters from the aluminum layer. But 
still the problem with the ground potential variation exists. The simplest way to eliminate 
the problem with ground potential variations is to provide an individual ground lead for 
each heater that connects to a ground bus bar. This bus bar must be large enough to 
provide less than 100 ^iV voltage difference between individual heater ground 
connections during all operating conditions. The construction steps are as follows: 

1 . A thin layer of titanium (Ti, 22) is first sputtered onto the quartz to enable the 
platinum (Pt, 78) to adhere to surface. 

2. A 2000 A layer of platinum is deposited on top of the titanium layer. 

3. The platinum and titanium are etched away to leave the serpentine platinum 
heaters and the power leads. 

4. A layer of aluminum is then deposited and etched away to leave aluminum 
overlapping the platinum for the power leads and the wire bonding pads. 

5. Finally, a layer of silicon dioxide is deposited over the heater array to provide a 
uniform energy surface across the heater. The area where wire-bond connections will 
later be made is masked off to maintain a bare aluminum surface. 

3.1.2 Heater Specification 

The finished heater array measures approximately 2.7 mm square. It has 96 
heaters on it, as shown in figure 3.1(c). Each individual heater is about 0.27 mm square. 
The lines of the serpentine pattern are 5 ^m wide, with 5 |im spaces in between the lines. 
The total length of the platinum lines in one heater is about 6000 |im, and the heater lines 
about 2000 A thick. The nominal resistance of each heater's resistance is 750 ohm. 



26 



Aluminum Ground Lead 



Silicon Dioxide Aluminum Power Lead 

Platinum Heater 




(a) 



^ 



(b) 



96 95 94 93 92 


91 


90 89 




65 37 64 63 62 61 


60 


59 58 


88 


66 38 17 36 35 34 


33 


32 57 


87 


67 39 18 5 16 15 

68 40 19 6 1 4 

69 41 20 7 2 3 

70 42 21 8 9 10 


14 
13 
12 
11 


31 56 
30 55 
29 54 
28 53 


86 
85 
84 
83 


71 43 22 23 24 25 


26 


27 52 


82 


72 44 45 46 47 48 


49 


50 51 


81 


73 74 75 76 77 


78 


79 80 





(c) 



Figure 3.1 Heaters and heater array, (a) Heater construction; (b) Single serpentine 
platinum heater; (c) Heater array with 96 heaters. 



27 

3.2 Constant Temperature Control and Data Acquisition System 

The system is consisted of feedback electronics circuits, interface print board 
connecting heaters array to the feedback electronics circuits, a D/A board used to set the 
heater temperature, two A/D boards for data acquisition, and software made from Visual 
Basics 6.0 in windows 95. 
3.2.1 Feedback Electronics Loop 

This experiment makes use of the relationship between platinum electrical 
resistance and its temperature. We know that resistance of the platinum almost varies 
lineariy with its temperature by the following relationship: 

(R-R)/R = C(T-T) (3.1) 

Where R is the electrical resistance at temperature T, Ro is the resistance at a 
reference temperature To and C is the constant coefficient. For platinum, the value of C 
is 0.002 Q/Q°C. The key part of the loop is the Wheatstone bridge with a feedback loop 
where Rh is the platinum heater. Each heater has a nominal resistance 750Q. For a 
temperature change of 1°C, the heater's resistance would change by 1.5Q, while R2, R3 
and R4 are regular metal film resistors which values are not sensitive to temperature. The 
resistance of the digital potentiometer. Re, can be set by the computer. Each heater has an 
electronic loop to regulate and control the power across it. Wheatstone bridge shown in 
figure 3.2 is used to carry out the constant temperature control. The bridge is said to be 
balanced when Vi = V2. This occurs when the ratio between R4 and Rh is the same as that 
between R2 and (Rc+Ra). The feedback loop maintains the heater at a constant 
temperature by detecting imbalance and regulating the current through the bridge in order 
to bring it back into balance. The amplifier will increase or decrease the electrical current 



28 

to the circuit until the heater reaches the resistance necessary for the bridge to maintain 
balance. Therefore, the exact value of Re corresponds to the temperature of the heater Rh. 




Dual Digital 
Potentiometer 



Figure 3.2 Wheatstone bridge with feedback loop. 

3.2.2 jxProcessor Control Board and D/A Board 

Each heater on the heater array can be individually controlled. ^Processor control 
card programs each of the 96 feedback control circuits with correct control voltage. 
Rather than having 96 separate wire connections from the computer control board, a 
multiplexing scheme is used, where a single wire carries a train of voltage pulses to all 
the boards and an address bus directs the voltage singles to the correct feedback circuit. 
D/A board is used to connect the computer for the software to send the addressing 
signals. The details can be referred to T. Rule, "Design, Construction, and Qualification 
of a Microscale Heater Array for Use in Boiling Heat Transfer", Master of Science thesis 
in mechanical engineering at Washing State University. 



■>^\.':. -'Jit 



29 

3.2.3 A/D Data Acquisition Boards 

Each of the A/D data acquisition boards used in this experiment has 48 channels. 
For 96 heaters, to acquire data simultaneously, we installed two A/D cards. But we just 
need one of them because maximum eight heaters were selected for the purpose of this 
research. The major parameters of the A/D cards have been shown in Table 3.1. 

Table 3.1 The specifications of the D/A cards 



# channels 


48 single ended, 24 differential or modified 
differential 


Resolution 


12 bits, 4095 divisions of full scale 


Accuracy 


0.01% ofreading+/-l bit 


Type 


successive approximation 


Speed 


micro- seconds 



3.2.4 Heater Interface Board (Docoder Board) 

Heater interface board is used to interface the heater array with the feedback 
control system. Since the heaters are independently grounded on the heater array, there 
are 192 wires extended from the heater array to the interface board, which are accessed 
by the feedback electronics loops. 

3.2.5 Software 

The software used in this experiment functions as following: 

1. Address heaters so that heaters can be selected. 

2. Send signals from the computer to the computer control board and D/A card to 
set the heaters temperature. 

3. Automatic and manual heaters calibration. 



30 

4. Data acquisition. 

The software is developed in the Microsoft Visual Basic 6.0 environment under 
windows 95 running in PC. 

3.3 Boiling Condition and Apparatus 

3.3.1 Boiling Condition 

In this experiment, we choose FC-72 to be the boiling fluid. The reason for 
choosing FC-72 is that it is dielectric, which makes it possible for each heater to be 
individually controlled. The bulk fluid is at the room condition (1 atm, 25°C), where its 
saturation temperature is 56°C, thus it is subcooled pool boiling. 

3.3.2 Boiling Apparatus 

Initially the boiling experiments were performed in an aluminum chamber. To 
improve the visualization results, a transparent boiling chamber was built. Another 
advantage of the new chamber is its flat glass walls that effectively prevent the image 
distortion taken by the fast speed camera described in section 3.4.2. Figure 3.3 shows the 
boiling experimental setup. In addition to heater array and electronics feedback system, 
the computer is used to select the heaters and set their temperature through D/A card and 
acquire data through A/D cards. 

3.4 Experiment Procedure 
3.4.1 Heater Calibration 
3.4.1.1 Calibration apparatus 

The calibration apparatus includes the constant temperature oil tank with oil- 
circulating pump and temperature control system, as shown in figure 3.4. The constant oil 
tank functions to impinge the constant oil into the heater array surface. The temperature 



31 



Not to Scale 




Digital camera 
for bottom view 



Figure 3.3 Boiling apparatus, 
control system is used to keep the circulating oil at a constant temperature. Calibration is 
the beginning of the experiment, and it is also a very important step since the following 
boiling experiment will be based on the calibration data. Therefore, much more care 
should be exercised to ensure the accuracy. 
3.4.1.2 Calibration procedure 

The calibration procedure is as follows: 

1. Set the temperature controller at a certain temperature. 

2. Circulating the fluids in the calibration tank. Power the heating components. 
After this, several minutes or more are needed to maintain the temperature of the 
circulating fluid at the stable temperature. 

3. Start the calibration routine in PC and calibrate. The computer automatically 
saves the calibration result. 



32 




Electronics feedback system 



(a) 



Temperature 
Controller 



TC 



DC power to SSR 



SSR 



_mtTfn„, 



o 



_v^ 



Fast blow fuse 



(b) 

Figure 3.4 Schematic of calibration apparatus and temperature control loop, (a) The 
calibration system; (b) The electrical loop to maintain the temperature of calibration oil. 



4. Set the heater array at another temperature. Follow the first and second steps till 
all calibration is completed. 

5. Two calibration methods are included, automatic method and manual method. 
Automatic method is for regular calibration use. We can select heaters to 

calibrate, though, normally we calibrate all 96 heaters at one time. To find the 
corresponding control voltage for the set temperature, progressive increment method was 
used. Increment the control voltage gradually, and compare the voltage output across the 



33 

heater with last time value. If the voltage across the heater is different from the last time 
value, we can say, the controlling system starts to regulate the circuit. Then the control 
voltage is the corresponding value for the set temperature. It is worth mentioning that 
how to set the difference to compare the voltage is important. Initially, the difference was 
set as 0.01. The result proves the control voltage is a little bit higher than the actual value. 
If the difference is set as 0.003, then the result is good. How to prove the result is the 
correct value for the set temperature, manual calibration method is used to check it out. 

Manual method is an alternative to the regular automatic method. It is designed to 
check the accuracy of the automatic method. By referring to the figure 3.5(a), we can see 
by increasing the control voltage, the heater's voltage starts to increase at about 91 axial 
value. Below 91, the heater's temperature is at the set temperature; the voltage across the 
heater is very small and at a relatively constant level. Starting at 91, increasing the 
control voltage will increase the heater's voltage so that heater's temperature increases 
accordingly. The starting value of 91 is the control voltage corresponding to the set 
temperature. This method is much more viewable than automatic method. Its 
disadvantage is slow, only one heater can be done at one time. But we can rely on its 
result to verify the accuracy of automatic method. 
3.4.1.3 Calibration results 

Based on the relations between the heater resistance and temperature indicated in 
Eq. (3.1). For each heater, its resistance almost linearly changes with temperature. Thus, 
ideally, the resistance-temperature figure is an approximately straight line. The slope of 
the line is determined by the material property. Thus the lines representing the resistance- 
temperature relations have almost the same slope. On the other hand, the temperature 
change also depends on heater's initial resistance values. This regard is shown on figure 



34 

3.5(b) for calibration results of heaters #1 through #9, where the slope of the lines for 
different heaters. 



3.5 



a 2.5 

a 

c 

I ^ 

E 

£1.5 



S 1 

o 

> 



0.5 - 



Voltage acquired from the heater vs. DQ values 



DQ value for this heater 
at this temperature (91 ) 



♦ o ' o a CO do o o ' d ho 




100 150 

DQ value (digital pot) 



200 



(a) 



Calibration results for heaters (1 -9) 
from SOX to120X 




60 70 80 90 100 110 

Impinging liquid temperature (°C) 



250 



(b) 



Figure 3.5 Part of the calibration results, (a) Result of the manual calibration method; 
(b) The calibration results (only heaters #1 through #9 were shown). 



35 

The calibration results obtained for each heater will be used in boiling experiment 
to set heater temperatures. For the present research, the heaters will be always set at the 
same temperature in any experiment performed, thus nominally, there will not be any 
temperature gradient among heaters. 
3.4.1.4 Comparison of calibrated resistances with the calculated resistances 

To validate the calibration results, i.e. the temperature of the heaters obtained by 
calibration, we have measured the resistances of each heater at different temperatures and 
then compare them with the resistances from calculation using the platinum property 
relation given by Eq. (3.1), the result is shown in figure 3.6. From the above comparison, 
we conclude that measured resistances match well with calculated resistance. It implies: 

(1) The heater temperature is reliable. 

(2) We can use calculated resistance to evaluate heat dissipation with only a small 
uncertainty introduced. 



1030 

1000 
970 
940 
910 
880 
850 



■ Calculated R 
D Measured R 




50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 
Temperature °C 



Figure 3.6 Comparison of calibrated resistances of heater #1 with the calculated 

resistances from property relation. 



^■'.. .j»^ -i *«*■ _'- 



36 

3.4.2 Data Acquisition and Visualization 

To investigate the bubble coalescence, we need to generate bubbles with 
appropriate separation distances. Since each of the 96 heaters on the heater array is 
individually controlled by the electronic feedback control system, we can set active one 
or more of the heaters by powering them individually so that they reach a certain 
temperature while leaving all other heaters unheated. To obtain different cases of bubble 
coalescence, all we need to do is to select heaters. In reference to figure 3.1, by powering 
two heaters such as heaters #1 and #11, we obtain dual bubble coalescence. Also, if we 
choose #1 and #3, we obtain dual bubble coalescence with a shorter separation distance. 
However, by powering two heaters that are too far apart such as #1 and #25, two single 
bubbles will be generated, but the bubble departure sizes are not large enough for them to 
touch and merge before they depart. Therefore, for coalescence to take place, the active 
heaters have to be close enough within a certain range. The power consumed by the 
heater was acquired by the computer data acquisition system (figure 3.3). Data were 
acquired at a sampling rate of 40,000 Hz for each channel of the A/D system, after 
allowing the heater to remain at a set temperature for 15 minutes. The data were found to 
be repeatable under these conditions. The acquired data were converted to heat flux from 
the heater according to the following basic relationship: 

q"=(VyR)/A (3.2) 

For each heater configuration, the heaters were always set at the same temperature 

for the bubble coalescence experiment, and this temperature is varied to investigate the 

effect of heater superheat on the bubble coalescence. For all cases, the dissipation from 

heaters was acquired in sequence. Because steady state has been reached in all these 



37 

experiments, sequential data acquisition does not affect the data accuracy. The bubble 
visuahzation includes both bottom and side views; though bottom views are more 
suitable for multiple bubble coalescence. The semi-transparent nature of the heater 
substrate made it possible to take images from below the heater. The setup of experiment 
has been shown in figure 3.3. A high-speed digital camera (MotionScope PCI 8000S) was 
used to take images at 2000 fps with a resolution of 240 x 210, with maximum 8 seconds 
of recording time. The bubble visualization was performed using the shadowgraph 
technique. In this technique, the bubbles were illuminated from one side while the images 
were taken from the other side. 

3.5 Heat Transfer Analysis and Data Reduction 
3.5.1 Qualitative Heat Transfer Analysis 

Each heater has a dimension of 0.27mm x 0.27mm. For such a small heater, the 
heat transfer behavior is hardly similar to that for large heaters. Specifically, the edge 
effects greatly affect the heat transfer. Since the heaters used in our experiment are 
always kept at a constant temperature, the data reduction turns out to be much simpler. 
Qualitatively, the heat dissipated from the heater at a certain temperature, by reference to 
figure 3.7(a), is composed of the following components: 

1. Boiling heat transfer from the heater in boiling experiment, when the heater is 
superheated high enough. 

2. Conduction to the substrate on which the heater is fabricated. This is due to the 
temperature gradient between the heater and the ambient through the substrate. 

3. Radiation heat transfer due to the temperature difference between the heater 
and ambient. 

4. Natural convection between the heater and air and FC-72 vapor mixture when 
the heater array is positioned vertically to be separated from the liquid for data reduction 



38 

experiment. This natural convection is replaced by the boiling heat transfer from the 
heater when the boiling occurs on the heater surface. 

3.5.2 Data Reduction Procedure 

To obtain the heat transfer rates due to boiling only, we conduct the experiments 

by the following procedure: 

1 . Measure the total heat flux supplied to the heater during the boiling process at 
different heater temperatures. 

The total heat flux with boiling: 

q"rawl = q"top + q"condl + q"radl. (3.3) 

2. Tilt the boiling chamber 90°, so that the heater is exposed to the air and FC-72 
vapor, while separated from FC-72 liquid, and measure the total heat flux without boiling 
at corresponding temperatures. 

Therefore, the total heat flux without boiling: 

q"raw2 = q"natural + q"cond2 + q"rad2 (3.4) 

The q"condi in Eq.(3.3) and q"cond2 in Eq.(3.4) are the conduction to the substrate 
and ambient through the substrate. Because the heater is held at a constant temperature, 
they are independent of the state of fluid above the heater, thus we assume q"condi=q"cond2. 
The same reasoning also goes with radiation. Thus, from Eq.(3.3) and Eq.(3.4) the heat 
dissipated above the heater during boiling can be derived as the following: 

q top=q rawl - q raw2+q natural (3.5) 

where q"naturai is the contribution from natural convection with the mixture of air and FC- 
72 vapor. To get a good estimate of the natural convection component in Eq.(3.5), we 
need to pay special attention to the small size of the heater we used. The details for this 
estimation are given in the following. 



39 



Bulk liquid 



Bubble 



I top 







\. ^~~*- Icondl 


/ 


\ 



Ambient room 
(a) 





Substrate 


\ 


% 


Ambient room 


w 




q'(!ond2 



qrad2 



Mixture of air 
and vapor 



natural 




(b) 



Figure 3.7 The schematic showing the heat dissipation from a heater, (a) The heat transfer 

paths from the microheater during boiling experiment; (b) The heat transfer paths from 

the heater during data reduction experiment. 



40 

3.5.3 Determination of Natural Convection on the Microheaters 

We have done a significant amount of literature research in order to rationally 
determine the natural convection on the heaters we were using. We first use the empirical 
correlations to evaluate the heat dissipated from the heater, in which we use the results of 
Ostrach (1953) to calculate this natural convection. Then the calculated heat dissipation is 
used to compare with experimental results. 

Conduction. We assume one dimensional conduction from the heater to the 
ambient through the quartz substrate. The ambient has a constant temperature of 25°C. 
Conductivity of the quartz substrate is ksub = 1 -5 w/mK. For different heater temperatures 
To, using Fourier law of conduction, we calculate the conduction heat flux. For 
simplicity, we neglected the epoxy thickness that is used to seal the heater at the bottom. 
Since we calculate the conduction based on quartz substrate only, neglecting the heat 
transfer resistance of epoxy, the calculated conduction heat transfer should be larger than 
that if the epoxy layer is accounted for. 

Convection. When the liquid was separated from the heater, there is natural 
convection heat transfer to the mixture of air and vapor from the heater. For this 
calculation, the mixture of FC-72 vapor and air is approximated as ideal gas of air. 

Radiation. With the approximation of black body, the radiation heat flux is 
calculated as follows: 

q" = a{Ts'-To^) (3.6) 

where cr is the Stefan- Boltzmann constant. 

The calculation results for the above heat transfer modes have been shown in 
figure (3.8). From this figure, obviously, the sum of convection, conduction and 



41 




90 120 

Heat temperature (°C) 



Figure 3.8 Heat flux comparison from experimental and calculation results. 



radiation is far less than the total heat flux q"raw2, when the heater is separated from the 
liquid. This is sufficient to prove that since the heater size is much smaller than the 
regular heater size, classical horizontal isothermal correlation is not applicable for this 
heater. We need to find another approach to evaluate the natural convection occurring 
from the heater for the data reduction. 

Baker (1972) has investigated the size effects of heat source on natural 
convection. He argued that as the heat source area decreases, the ratio of source perimeter 
to surface area increases and since substrate conduction is proportional to the source 
perimeter, the portion of the heat transferred by conduction into the substrate increases as 
the surface area decreases. In our experiment, since the heater is kept at the same constant 
temperature both in boiling and no-boiling conditions, the conduction to the substrate 



42 

should be the same regardless of the condition on the surface of the heater. However, this 
small size effect does affect the natural convection calculation in our data reduction. 
Baker (1972) used the experimental setup similar to that used in this research to study 
the forced and natural convection of small size heat source of 2.00 cm^, 0.104 cm^ 
and 0.0106 cm , respectively, smallest of which is over 10 times larger than the heater 
used in this experiment. Therefore, we can not use Baker's data in our experiment. Also 
according to Park and Bergles (1987) and, Kuhn and Oosthuizen (1988), due to the small 
size, the edge effects are important. The approach to determining ^"natural in this study for 
a heater with height L and width W is that we first used the results of Ostrach (1953) for 
two-dimensional laminar boundary layer over a vertical flat plate with a height of L. Then 
the two-dimensional Nusselt number is corrected for the transverse width of W by the 
correlation developed by Park and Bergles (1988). The following provides the details of 
the procedure. The Grashof number, Gri, at the trailing edge of a vertical plate with 
height L is defined as 

where )3 is the coefficient of thermal expansion, T^ is the heater temperature, T, is 

the ambient fluid temperature, L is the heater length, and v is the kinematic viscosity of 
the fluid. 

Based on Ostrach (1953), the local Nusselt number at the distance L from the 
leading edge of the heater surface is given by : 



Nu,= 



V 4 ; 



g(Pr) (3.8) 



43 



where g(Pr) is a function of the Prandtl number, Pr, of the fluid and is given by 
LeVevre (1956) as below : ' /* 

g(Pr) = ^JJ^ (3.9) 

(0.609 + 1.221Pr^ + 1.238Pr)^ 



The average Nusselt number jVm^ of the heater surface with a height of L can be 
obtained by : 



Nu,=-Nu, ._ (3.10) 

This two-dimension Nusselt number needs to be corrected to take into account the 
finite width effects. This correction is based on the relation given by Kuan and 
Oosthuizen (1988), which is repeated here : 



Nu, , = Nu, X 



-|0.4752 

, 362.5 
1 + 



Ra 



w 



(3.11) 



In the above. Raw is the Rayleigh number based on the width W of the heater and 



Raw is equal to Grw x Pr. This corrected Nusselt number A^m^^^^^ has been used to 

evaluate the natural convection heat transfer from the microheaters. 

The derived natural convection heat fluxes for different heater configurations are 
given in figure 3.9 and they were used in equation (3.3) to find the boiling heat transfer 
flux, q"top- The order of magnitude of the derived natural convection heat fluxes using the 
above approach has been found to be consistent with the results given by Kuan and 
Oosthuizen (1988), where they investigated numerically the natural convection heat 
transfer of a small heat source on a vertical adiabatic surface positioned in an enclosure 
which is very similar to our experimental condition. 



44 



10 
9 
8 

o 
S. 6 

X 

n 

« 4 

X 



Natural convection heat flux derived for 
- heaters in this experiment 



Single heater, L=0.027cm 
Two heaters, L=0.038cm 
Three heaters, L=0.047cm 
Four heaters, L=0.054cm 
Five heaters, L=0.061cm 




2 r 
1 - 



'''''*''''*''''*''''*''''*''''*''''*''''*''''*''''*''''*'''' * 
40 50 60 70 80 90 100 110 120 130 140 150 160 



Heater temperature (AT) 



Figure 3.9 Derived natural convection heat fluxes for different heater configurations. 

3.5.4 Uncertainty Analysis 

Uncertainty analysis is the analysis of data obtained in experiment to determine 
the errors, precision and general validity of experimental measurements. 

For single sampled experiments, the methods introduced by Kline and 
McClintock (1953) have been popularly used to determine the uncertainty. The theory of 
the method is introduced in the following. 

Assume ^ is a given function of the independent variables xi, X2, xj, ... x„, that is, 
R = R{xi, X2, X3, ... Xn). Let wr be the uncertainty in the result of R, and wi, wz, w^, ... Wn, 
be the uncertainties in the independent variables. If the uncertainties in the independent 
variables are all given with the same odds, then the uncertainty in the result with these 
odds is given as: 



\^ 



< V 



•Uoo^.c 



ffh. 



45 



w„ = 



BR 

dx, 



■w, 



+ 



dR 



■W-, 



(dR 
dx. 



•w. 



+ •■• + 



[dR 
dx„ 



1/2 



■w„ 



(3.12) 



Because of the square propagation of the separate uncertainties, it is the larger 
ones that predominate the final uncertainty. Thus any improvement in the overall 
experimental result must be achieved by improving the instrumentation or technique 
connected with these relatively large uncertainties. It should be noted that it is equally as 
unfortunate to overestimate uncertainty as to underestimate it. An underestimate gives 
false security, while an overestimate may make one discard important results, miss a real 
effect or buy too much expensive instruments. The purpose of this exercise is to analyze 
the possible sources of uncertainties and give a reasonable estimate of each uncertainty, 
and finally obtain the overall uncertainty. 

In each experiment, the heaters are always set at the same temperature, and this 
temperature was increased to investigate how the boiling heat transfer changes with 
heater temperature. The boiling data are always associated with the pre-set temperature. 
Therefore, the uncertainties will include uncertainty for heater temperature and 
uncertainty for boiling heat transfer. 

The uncertainty sources come from calibration, boiling and data reduction 
experiments. They have been summarized in the following. 

The uncertainty sources from calibration. The uncertainty sources from 
calibration basically include the oil fluctuation in the calibration chamber, heat loss due 
to oil impinging on the heaters, discrete increment of control resistance and slew rate of 
the opamp which is used to balance the wheat-stone bridge. Each uncertainty for these 
has been estimated and given in table 3.2. 



46 

Table 3.2 The uncertainty sources from calibration 



Sources of uncertainty 


Estimated uncertainty value 


Oil temperature fluctuation 


Cti = +0.5°C 


Heat loss due to oil impinge 


En = +0.05°C 


Discrete increment of control resistance 


eT3 = +o.rc 


Slew rate of Opamp 


Negligible 



The uncertainty sources from boiling experiment. To have a better idea of 
uncertainty sources from boiling experiment, figure 3.10 needs to be referred. They 
include: 

(1) Wiring resistance from heater to feedback system and from feedback system 
to A/D card. Estimated total wiring resistance is about 50 ohm. Since heater's nominal 
resistance is 1000 ohm. Thus uncertainty introduced is 5%. 

(2) A/D card resolution, 2.44mV: 12 bits 4095 divisions of full scale (lOV). For 
present experiments, the average voltage is about lOV. Thus the uncertainty is 
2.44mV/10V, which is less than 0.03%. 

(3) Voltage division device. Mainly comes from the deviation of two division 
resistors. They are metal film resistors (1% accuracy). Thus, the voltage division 
uncertainty can be 101%/99% = 1.02%. 

Summary of uncertainty sources in this experiment. The uncertainty sources 
analyzed above can be divided into uncertainty sources for heater temperature and for 
heat flux. They are summarized as follows. 

(1) Uncertainty sources for temperature 

- Oil temperature fluctuation in calibration, Cji = +0.5°C. 



47 




Figure 3.10 The circuit schematic for temperature control and voltage division. 



- Discrete increment of control resistance, £72 = +0.05°C. 

- Drift of Voff of the opamp, £73 = +0. 1°C. 

- Temperature fluctuation during boiling, especially during the vapor-liquid 
exchange process, £74 = +0.05°C. 

(2) Uncertainty sources for boiling heat transfer 

- Wiring resistance, £vi = 5%. 

- Resolution of A/D card, £v2 = 0.03%. 

- Voltage division device, £v3 = 1.02%. 

- Natural convection, £hi = 15%. 



48 



Determination of overall temperature uncertainty. Since the individual 
uncertainties given above are absolute values relative to one variable (temperature), the 
overall temperature uncertainty can be obtained by simply summing up each of them, that 
is: Ct = exi + £12 + £t3 + £t4 = 0.5°C + 0.1°C + 0.05 °C + 0.05°C = 0.7°C. 

Determination of overall heat transfer uncertainty. From the uncertainty 
sources for boiling heat transfer analyzed above, the first three parts come from the 
voltage measurements. Since they come from the single variable, the total uncertainty for 
voltage can be obtained: 

ev = evi + £v2 + ev3 = 5% + 0.03% + 1.02% = 6.05% 

Now we are ready to calculate the overall uncertainty for boiling heat transfer. 



" _ ^ raw\ 



^top = 



RA RA 



raw! 1 ^^ 



natural 



(3.13) 



From Eq. (3.7), the total boiling heat transfer is a function of voltages and natural 
convection, neglecting the uncertainties contributed by R (resistance of heaters) and A 
(area of the heaters). 

From the uncertainty theory, the overall uncertainty can be written as 



w. = 

1 



^a,' 

a^"- 



+ 



dq" 



dv 



•w„ 



+ 



dq 



[H 






that is. 



w . 



RA 



\- 



raw\ V 



+ 



r_2_ 

RA 



raw 2 v„, 



+{w. y 



In this equation. 



w^ =£, xV .,w =f:^xV ,,w. =e xfl' 



49 

In this experiment, the temperatures of the heaters are set in a temperature range, 
thus R is changing. To calculate uncertainty, we let R = 1000 ohm. Also the areas of the 
heaters are given as A = 0.00073 Icm^. The averaged values for voltages during boiling 
and data reduction are given at Kawi = lOV, Kaw2 = 4V. With these data, we can 
calculate the overall uncertainty at different temperatures. As an example, at 100°C single 

bubble boiling: ^'„,„„, = 40w/cm^ . 

The overall uncertainty can be obtained as w^- = 9.2w/cm^ . 

Also, at 100°C, the boiling heat transfer can be read from the boiling curve: 

q' = 65w/cm^ . 

Thus, the percent uncertainty for boiling heat transfer at 100°C can be obtained 
readily as: 

Woverall = 9.2/65 = 13.8%. 

For other temperatures, the uncertainty can be calculated following the same 
procedure. For the single bubble boiling, the boiling heat transfer uncertainties at 
different temperatures have been calculated and shown in the figure 3.1 1(a). 

For dual bubble coalescence, we also calculated the overall uncertainty levels for 
boiling heat transfer for temperatures from 100°C to 140°C, which are shown in the 
figure 3.1 1(b) with the overall uncertainty values for single bubble boiling shown as well 
for comparison. 

As we have observed that in the dual-bubble coalescence boiling case, the overall 
uncertainty is smaller than that for the single bubble boiling at corresponding 
temperatures. The reason for this can come from two factors: (1) due to bubble 



50 



17% 

16%- 

15%- 

14%- 

13%- 

12%- 

11%- 

10%- 



El % Uncertainty 



I I I I I I I I F'-'N^— '^' "i ' 'i 
100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 



(a) 



17% 

16%- 

15%- 

14%- 

13%- 

12%- 

11%- 

10% 



D% Uncertainty for single bubble 

■ % Uncertainty for dual-bubble #1 with #1 1 . 




100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 



(b) 



Figure 3.11 The uncertainty at different temperatures, (a) The uncertainty for single 
bubble boiling at different temperatures; (b) The uncertainty for dual-bubble coalescence 

together with single bubble boiling. 



51 

coalescence, the overall boiling heat transfer has been increased. (2) due to heater 
interaction, the natural convection is smaller for the single heater case. 

In summary, for temperatures, the oil temperature fluctuation during calibration 
contributes to the main uncertainty, though opamp offset also has some contributions. 
Natural convection is the main contributor to the boiling heat transfer uncertainty. The 
overall uncertainty for heater temperature is estimated about 0.7°C, and the overall 
uncertainty of boiling heat flux is about 15% between 100°C ~ 170°C, and this 
uncertainty is temperature dependent. The uncertainty of dual bubble boiling is smaller 
than that of the single bubble boiling due to coalescence-enhanced heat transfer. 



CHAPTER 4 
SINGLE BUBBLE BOILING EXPERIMENT 

4.1 Introduction 

Applications of microtechnology must utilize components or systems with 
microscale fluid flow, heat and mass transfer. As the size of individual component 
shrinks and the length scale decreases drastically, the transport mechanisms involved go 
beyond those covered by the traditional theories and understanding. The development of 
the new theories and the fostering of up-to-date physical understanding have fallen 
behind the progress of micro machining and manufacturing. Extensive survey papers 
(Duncan and Peterson, 1994, Ho and Tai, 1998) of microscale single-phase heat transfer 
and fluid mechanics noted that an investigation of the flow characteristics of small 
channels has shown significant departure from the thermo-fluid correlations used for 
conventional macroscale flows. For example, for turbulent flow of gases in microtubes 
(with diameters of 3 mm to 81 mm), neither the Colbum analogy nor the Petukhov 
analogy between momentum and energy transport (Duncan and Peterson, 1994) is 
supported by the data. More recently Gad-el-Hak (1999) gave a complete review on the 
fluid mechanics of microdevices. He concluded that the technology is progressing at a 
rate that far exceeds our understanding of the transport physics in micro-devices. 
Therefore the study of micro-scale transport has become an integral part of not only 
understanding the performance and operation of miniaturized systems, but also designing 
and optimizing new devices. The current chapter presents an experimental study and 
analysis to provide a fundamental basis for boiling on a microheater and to investigate the 

52 



53 

small size effect on boiling mechanisms. Microheaters have been found in many 
applications, for example, Inkjet printerhead, and actuators and pumps in microfluidic 
systems. 

Recently Yang et al. (2000) proposed a new model of characteristic length scale 
and time scale to describe the dynamic growth and departure process of bubbles. A 
correlation between bubble departure diameter and bubble growth time is established and 
a predication formula for bubble departure diameter is suggested by considering the 
analogue between nucleate boiling and forced convection. The predictions by the model 
agree well with experimental results that were obtained with basically macro-scale pool 
boiling conditions. Rainey and You (2001) reported an experimental study of pool 
boiling behavior using flat, microporous-enhanced square heater surfaces immersed in 
saturated FC-72. Flush-mounted 2cm x 2cm and 5cm x 5cm copper surfaces were tested 
and compared to a 1cm x 1cm copper surface that was previously investigated. Heater 
surface orientation and size effects on pool boiling performance were investigated under 
increasing and decreasing heat-flux conditions for two different surface finishes: plain 
and microporous material coated. Results of the plain surface testing showed that the 
nucleate boiling performance is dependent on heater orientation. The nucleate boihng 
curves of the microporous coated surfaces were found to collapse to one curve showing 
insensitivity to heater orientation. The effects of heater size and orientation angle on CHF 
were found to be significant for both the plain and microporous coated surfaces. Hijikata 
et al. (1997) investigated boiling on small heaters to find the optimum thickness of the 
surface deposited layer to enhance the heat removal from the heater in order to obtain the 
best cooling effect for a semiconductor. The square heaters they used are 50 fim and 100 



54 

l-im and they claimed that the deposited layer conduction dominates the heat transfer due 
to the small sizes of the heater area. Also they presented the nucleate boiling curves for 
the two heater sizes and different deposited layer thickness. Rule and Kim (1999) used a 
meso-scale heater (2.7mm x 2.7mm) which consists of an array of 96 microheaters. Each 
of the microheaters was individually controlled to maintain at a constant temperature that 
enabled the mapping of the heat flux distributions during the saturated pool boiling of 
FC-72 fluid. They presented space and time resolved data for nucleate boiling, critical 
heat flux and transition boiling. Specifically, the outside edge heaters were found to have 
higher heat fluxes than those of the inner heaters. For the materials in this chapter, only 
one single microheater (marked as #1 in figure 3.1) is heated to produce bubbles. The 
experiment starts with setting the microheater at a low temperature of 50°C where only 
natural convection occurs at this temperature. Then the temperature of the heater is 
incremented by 5°C at a time, and for each increment, the heat dissipation by the heater is 
obtained by the data acquisition system until the superheat reaches 1 14°C. 

4.2 Experiment Results 

For each series of the boiling experiment, the heater temperature was set at 50°C 
initially. After that the temperature was increased with 5°C increments until it reached the 
superheat of 114°C. For each temperature setting, the voltage across the heater was 
sampled at a rate of 4500 times per second. The time-resolved heat flux was obtained 
based on the heater area and its electrical resistance. 
4.2.1 Time-averaged Boiling Curve 

Figure 4.1 shows the measured boiling curve in logarithmic and linear scales 
where the superheat of the heater covers a range from -6°C to 1 14°C. As the degree of 



55 

superheat was increased to 54°C, single bubbles were seen to nucleate. The onset of 
nucleate boiling (ONB) for the single bubble experiment was found at the superheat AT^, 
of 54°C to 59°C. After the ONB, the degree of superheat for boiling dropped to 44°C as 
the minimum temperature for stable boiling on this heater. It is noted that the trend of 
figure 4. 1 remains very similar to that of the classical pool boiling curve predicted by 
Nukiyama (1934) and this includes the ONB phenomenon. In figure 4.1, similar to the 
classical macro-scale boiling, the entire boiling curve can be divided into three sections. 
Regime I is due to natural convection. Regimes II and III are separated by the peak heat 
flux (critical heat flux) which takes place at a heater superheat AT^, of 90°C. Also shown 
in figure 4.1 are the boiling data from Rule and Kim (1999) for a meso-scale heater 
(2.7mm x 2.7mm) which is composed of a 10 x 10 array of 96 microheaters. It is noted 
that the boiling heat transfer rates for a micro heater (0.27 mm) in the current work are 
more than twice higher than those for a meso-scale heater (2.7 mm) but the general trends 
are similar for both heaters. Also, the peak heat flux for a micro heater takes place at a 
higher heater temperature. These results are consistent with those of Baker (1972) for 
forced convection and natural convection that as the heater size is decreased the heat 
transfer increases. 
4.2.2 Time-resolved Heat Flux 

Figure 4.2 shows the heat flux history when the microheater was set at a degree of 
superheat of 44°C. In figure 4.2, we note that the heat flux is closely associated with the 
bubble life cycle during the ebullition process. [A] corresponds to a large spike that takes 
place during the bubble departure. When the preceding bubble departs, the heater is 
rewetted by the cooler bulk fluid. The establishment of the microlayer for the succeeding 



56 



•»J - 


peak heat flux 




JP 


40- 


V 


35 - 


- X Before ONB^ n^jjjj 


rC 


DRun 1 rf^ 


-yao 


ARun2 ^ g 


t 


0Run3 


s 


Meso heater (Rule and Kim. 1 ^) 


S 


OX ■ 




t 0° X 


20 


O O rn 




>« ' ' 




OX 




o 


15 


^ o 


10 





-10 10 30 50 70 90 110 130 
Superheat AT 



(a) 



100 
90 
80 
70 
60 
"g 50 

X 

3 
(S 

S 30 



ao 



10 



X Before ONB 




DRun 1 






ARun2 






ORun3 






O Meso heater (Rule and Kim, 1 999) 






j^eak heat flux 




mj 


'« 


■ 


Ef 


D 


■ 


<^ll] 




X 





I« 100 

Superheat AT 



1000 



r> 



(b) 



Figure 4.1 The boiling curve of the single bubble boiling, (a) The boiling curve in 
linear scale; (b) The boiling curve in logarithmic scale. 



r 






1M 

100 
^ 80 
S 60 

♦^ 
ID 
« 40 

20 





57 




Heat flux trace for a typical bubble cycle from #1 at AT=44°C 

[F] 



JDL 



i!lA^ 




1.5 



2 2.5 3 

Time (seconds) 



3.5 



Figure 4.2 The heat flux variation during one bubble cycle. 



new bubble on the heater surface and the turbulent micro-convection induced by this 
vapor-liquid exchange lead to this large heat flux spike. [B] represents the moment when 
the succeeding bubble starts to grow after the vapor-liquid exchange. As the new bubble 
grows, the contact line that is the three-phase division expands outward. The bubble 
growth results in a larger dry area on the heater surface, thus the heat flux is decreasing. 
The low heat flux period indicated by [C], [D] and [E] corresponds to the slow growth 
stage of a bubble. As the bubble size reaches to a certain level, the buoyancy force starts 
to become more important than the forces which hold the bubble to the surface, but it is 
still not large enough to lift the bubble from the heater surface, causing the bubble to 
neck. During the necking process, the contact line starts to shrink, then the dryout area is 
starting to decrease, thus we have observed that the heat flux is starting to increase 
slightly with some oscillation of a small-amplitude. Finally, the buoyancy force is large 
enough to detach the bubble from the heater surface, and then another bubble ebullition 
cycle begins. 



58 

4.2.3 Time-resolved Heat Flux vs. Superheat AT 

Figure 4.3 shows the time-resolved heat flux at different heater superheats (44°C 
to 114°C with increments of 10°C) for a total of six-second data acquisition. Figure 4.4 
shows the trends of two characteristic heat fluxes during a bubble life cycle (Point A - 
Point E in figure 4.2) at various heater superheats. The curve with triangles represents the 
peak heat flux of a spike or the minimum heat flux of a dip during the bubble departure 
(point A). Based on figure 4.3, the bubble departure was recorded to produce a spike for 
the heater temperature up to 84°C, after that a heat flux dip was observed. In figure 4.4, 
The curve with diamonds shows the heat flux level during bubble slow growth (point E). 
It is clear that the two curves hold opposite trends, which is due to different controlling 
mechanisms as explained next. 

As we examine figures 4.1, 4.3 and 4.4 closely, all three figures consistently 
indicate that Regimes II and III are dominated by two different transport mechanisms. In 
figure 4.1, the heat flux increases with increasing heater superheat in Regime II while the 
trend reverses in Regime III. In figure 4.3, we notice that a heat flux spike is associated 
with the bubble departure in Regime II (heater superheat up to 84°C) and a heat flux dip 
is seen to accompany the bubble departure in Regime III. In figure 4.4, we found that the 
two curves cross each other at the heater superheat of 90°C which is the separating point 
between Regimes II and III. We believe that in Regime II bubble growth is mainly 
sustained by the heat transfer mechanism of microlayer evaporation that follows the 
rewetting of the heater surface. This scenario is supported by the presence of a heat flux 
spike recorded during the bubble departure. The spike is produced when the heater 
surface is rewetted by the liquid with micro turbulent motion which in turn causes the 
microlayer to form and the evaporation of the microlayer facilitates the bubble 



59 



110 

100 

-^ 90 

Ol 

1 80 
I 70 

3 60 
% 50 


#1 at AT=44''C Max: 1 05.6 w/cm', Min=44.7w/cm' 

1 , [ 


..mK^ 




X 40 
30 
20 








C 


) 0.5 1 


1.5 2 2.5 3 3.5 4 4.5 
Time (second) 


5 5.5 


6 



110 
100 

«-- 90 

"g 80 

I 70^ 

3 60 

1 50 ^ 

o 

I 40 

30 

20 




#1 at AT=54°C Max: 94.8w/cm', Min=47.1 w/cm' 




_aJv_.-^ ^j/^ 



I . ■ I ' ■ I I ■ ■ ■ I 



III I— 1_J ■ ■ I 



0.5 1 1.5 2 



2.5 3 3.5 

Time (second) 



4 4.5 5 5.5 6 



110 

100 

^ 90 

"i 80 

J, 70 

I 60 

1 50 

o 

X 40 

30 

20 t 



#1 at AT=64°C Max: 84.6w/cm', Min=48.9w/cm' 




L J_ 



_ I 



I ■ ■ . . t 



-tM^ ^-~~ 



0.5 1 1.5 2 



2.5 3 3.5 4 

Time (second) 



4.5 5 5.5 6 



110 

100 

^ 90 

~i 80 

I. 70 

3 60 

«: 

15 50 

a> 

X 40 

30 

20 




#1 at AT=74°C Max: 74.8w/cm', Min=51 .4w/cm' 



J'^~'»-«w_ . .^^ ^■*"*'>*.<- ^ . j j! ^••^j-'-.k^ 



I I '''!''' 'I ' I ' I I I I I , , I . . . . I , . . , I . . . , I , , , , I , . , , I 



0.5 1 1.5 2 



2.5 3 3.5 

Time (second) 



4.5 5 5.5 6 



Figure 4.3 Time-resolved heat flux variation at different heater superheats. 



60 



110 
100 

rf- 90 
"i 80 
2. 70 

5 60 

To 50 

I 40 r 

30 

20 



#1 at AT=84°C Max: 65.6w/cm', Min=53.2w/cm' 



L-wJFIf'^'^^*--^^^^ 



fill ^J_j , , i I I I ^-Lj I , t_l_j ■ ■ I ■ ■ ■ ■ ' I I l_^ , , I , , u 



0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 

Time (second) 



110 

100 

^ 90 

"i 80 

1. 70 

3 60 


- 




#1 atAT=94X 


Max: 47.8.6w/cm', Min=57.1 w/cm=' 








I 40 
30 
20 


. --Y'— 




-v-y— 


' Y" ■ ' 








c 


) 0.5 


1 


1.5 2 


2.5 3 3.5 4 4.5 


5 


5.5 


6 



Time (second) 



110 


- 






#1 at AT=104°C Max: 39.2w/cm', Min=47.9w/cm' 






100 


- 












,- 9° 


- 












1 80 
I 70 


' 






'*.. 






at flux 

g § 


- 












u 

Z 40 


- 




-v-Ny— 


■v-^ •■■>->- 




-V»-Y 


30 


- 












20 


'■ 


. . 1 




. 1 . : . . 1 , , , . 1 , , , . 1 . : . . 1 , , , . 1 . . . . 1 . . 


. . 1 . . 


. . 1 .... 1 


( 


) 


0.5 


1 


1.5 2 2.5 3 3.5 4 4.5 


5 


5.5 6 



Time (second) 



110 

100 \r 

"i 80 

^ 70 

3 60 

X 50 



40 
30 
20 



#1 at AT=1 1 4X Max: 33.7w/cm', Min=41 .5w/cm' 



i-y— 



^'-v.-y^ 



^'-w-y — 



-W-y— 



I I I I I I I i I I I ^-Lj ■■■'■■■■' , , ^_l , I , . I ■ . .. I .... I 



0.5 1 1.5 2 



2.5 3 3.5 

Time (second) 



4 4.5 5 5.5 6 



Figure 4.3~continued Time-resolved heat transfer variation at different heater superheats. 



V 



61 



120 


A Departing moment 




• O Minimum Growth 


100 


■ ^\,^^ Poly. ( Departing moment) 




^"^^ Poly. ( Minimum Growth) 


"6 ^ 
1 60 

9 


_A--^* — *^v — >^ 


1 40 


.-— ^--^^ 


20 











4 


50 60 70 80 90 100 110 120 




AT 



Figure 4.4 The trend of maximum and minimum heat fluxes during one bubble cycle with 

various heater superheats. 

« t* ■■ '' ' 

growth. While for Regime III, because of the higher heater superheat and the associated 
higher surface tension, the heater is covered by a layer of vapor all the time, even during 
the bubble departure. The heater surface is no longer wetted by liquid flow, which results 
in the bubble growth controlled by conduction through the vapor layer. The conduction- 
controlled scenario is supported by the presence of a heat flux dip recorded during the 
bubble departure in Regime III. The reason for this heat flux dip is mainly due to the 
necking process during the bubble departure. During the necking process, the top part of 
the bubble exerts an upward pulling force to stretch the neck. After the bubble severs 
from the base, the upward force disappears suddenly, which allows the lower part of the 
neck to spread and cover more heater surface area as depicted in figure 4.5. This larger 
dry area on the heater is responsible for the heat flux dip. Another support for the 



62 



Substrate 




„ f . _ / \ After departure 

Before departure / ] ^ 




leftover vapor stem 




Figure 4.5 A hypothetical model for bubble departure from a high temperature heater. 

conduction-controlled bubble growth in Regime III is that the heat flux level decreases 
slightly with increasing heater surface temperature which is caused by the decrease of 
FC-72 vapor thermal conductivity with increasing temperature. 

From figure 4.3, where each spike or dip represents the departure of a bubble, we 
can conclude that the bubble departure frequency increases with heater temperature. At a 
heater superheat of 44°C, the bubble departure frequency is about 0.43 Hertz, while at 
84°C, it is at 0.53 Hertz. Figure 4.3 also demonstrates the repeatability of the experiment. 

We observed that the bubble departure size did not change much with 
temperature. This is consistent with the results by Yang et al. (2000). Departure criteria 
of the bubbles are totally determined by the forces acting on the bubbles. Buoyancy force, 
besides the inertia force of the bubble, is the major player to render the bubble to depart. 
The interfacial surface tension along the contact line invariably acts to hold the bubble in 
place on the heater surface. Since this interfacial adhesive tension increases with 



63 

temperature, for departure to occur, it requires a larger bubble size to generate the 
corresponding buoyancy force to overcome the adhesive force. At higher temperatures, 
the thermal boundary layer that is due to transient heat conduction to the liquid is thicker 
which allows the bubble to grow larger. However, we observed that as the heater 
temperature was increased the bubble exhibited significant horizontal vibration that could 
be due to the higher evaporation rate at higher superheat. This vibration promotes bubble 
departure. On the other hand, due to the micro size of the heater, the natural convection 
taking place around the outside of the contact line helps bubble detach from the surface. 
Thus, these effects could cancel so that the bubble departure size does not change much 
with heater superheat. 
4.2.4 Visualization Results and Bubble Growth Rate 

Figure 4.6 provides a sequence of bubble images during the life cycle of a typical 
bubble on the microheater at superheat of 54°C. The images were taken from beneath the 
heater surface using a CCD camera of 30 fps. As shown by the images, as it grows, the 
bubble displays the shape of an annulus. The outer circle is the boundary of the bubble, 
which shows the diameter of the bubble. The inner circle represents the contact line 
where solid, liquid and vapor meet which measures the bubble base area on the heater. In 
this figure, we note that just before the departure, the micro heater is almost entirely 
covered by the vapor, thus resulting to a very low heat flux (the portion between point D 
and point E in figure 4.2), and at this point the bubble has a diameter of about 0.8 mm 
which is three times the size of the micro heater. The corresponding bubble size history 
and growth rate were estimated and plotted in figures 4.7 and 4.8, respectively. We note 
that the characteristics of bubble growth dynamics shown in figures 4.7 and 4.8 agree 
well with the theoretical prediction of Scriven (1959). 



64 




0.0333 



0.0667 



0.1000 



0.1333 




0.1667 



0.2000 



0.2333 



0.2667 





0.3000 



0.3333 



0.3667 



0.4000 




0.4333 



0.4667 



0.5000 



0.5333 




0.5667 



0.7000 



0.6000 



0.6333 



0.7667 



0.6667 




0.8000 



Figure 4.6 Bubble images of a typical bubble cycle taken from the bottom. 



65 




0.8333 



0.9667 



1.1000 



1.2333 



1.5000 



0.8667 



0.9000 



0.9333 




1.0000 



1.0333 



1.0667 




1.1333 



1.1667 



1.2000 







1.2667 



1.3000 



1.3333 




1.5333 



1.5667 



1.6000 



Figure 4.6~continued Bubble images of a typical bubble cycle taken from the 

bottom. 



66 



Bubble diameter vs. Time 




•q 0.3 
0.2 
0.1 
0.0 



Heater #1(0.07 136mm-) at AT=54°C 



O Diameter (mm) - reading 
2nd order polynomial trendline 



0.0 0.2 0.4 



0.6 0.8 1.0 1.2 1.4 1.6 

Time (seconds) 



Figure 4.7 Measured bubble diameters at different time. 



Growth speed of the single bubble at AT=54'C 



2.0 
1.8 
1.6 
1.4 
1.2 
1.0 
0.8 
0.6 
0.4 
0.2 
0.0 



The initial growth speed 
from to 0.0333 seconds 
is about 1 1.57mm/s. 



O Grow th Speed 
Logarithrric trendline 



Heater #l(0.07136mm2) at AT=54°C 



O 000 



0.2 0.4 0.6 0.: 



1 1.2 1.4 1.6 

Time (seconds) 



Figure 4.8 Bubble growth rate at different time. 



67 

A high-speed video camera has also been used to show the necking and bubble 
departure process. Figure 4.9 displays the images taken from the side and bottom views 
by the camera set at 1000 frames per second. Based on the side view images it is clear 
that the embryo of the next bubble is formed as a result of the necking process. It is also 
estimated that the bubble departs at a very high velocity of 0.16 m/s that causes a strong 
disturbance to the heater surface. This departure force in turn produces turbulent mixing 
and microlayer movement around the bubble embryo that are responsible for the spike of 
heat flux denoted as Point A in figure 4.2. As shown by the bottom view images, the 
bubble departure disturbance also produces microbubbles that stay near the bubble 
embryo and eventually coalesce with it. 

4.3 Comparison and Discussion 
4.3.1 Bubble Departure Diameter 

Recently Yang et al. (2000) proposed a dimensionless length scale and a 
corresponding time scale to correlate the bubble departure diameter and growth time. 
These scales are repeated in Eq. (4.1) and Eq. (4.2). 



r.. A ^A . 1 

d; = — ^ = — '- r =- 



kBj 



(4.1) 



where ^^ 2pATH^^ B = JaBa, 



(4.2) 



and , 



1 + - 

2 



ir ^ \ 



n 
^6Ja ^ 



2/3 



n 

+ 

6Ja 



For the current study, the measured bubble departure diameters and growth times at 
various heater surface superheats are given in table 4.1. It is shown that the bubble 



68 



Table 4. 1 Single bubble growth time and departure diameter 



AT 


49 


54 


59 


64 


69 


74 


79 


84 


89 


94 


99 


104 


Growth 

time 
(seconds) 


2.352 


2.054 


1.922 


1.873 


1.747 


1.611 


1.483 


1.403 


1.335 


1.237 


1.128 


1.024 


Departure 

diameter 

(mm) 


0.823 


0.824 


0.829 


0.833 


0.832 


0.836 


0.839 


0.843 


0.850 


0.859 


0.866 


0.875 



Table 4.2 Properties of FC-72 at 56°C 



Properties 


A (kg/m') 


Pv(kg/m') 


//fg (kJ/kg) 


Cp, (kJ/kg) 


«! (lO^mVs) 


Value 


1680 


11.5 


87.92 


1.0467 


3.244 



growth time is inversely proportional to the superheat while the departure size only 
increases very slightly with the increasing superheat as discussed above. 

In order to compare our data with the correlation of Yang et al. (2000), the data 
were converted to dimensionless forms according to Eqs. (4.1) and (4.2) using thermal 
properties given in table 4.2. Figure 4.10 shows the comparison. Part (a) of figure 4.10 is 
the reproduced correlation curve from Yang et al. (2000) and part (b) shows our data 
along with the correlation curve of part (a). It is seen that our data fall slightly lower than 
the extrapolated correlation of Yang et al. (2000). Since the data given in part (a) are 
from macro-scale heaters, we may conclude that on a microheater in the current study, 
the bubble departure size is larger and they stay on the heater longer. 
4.3.2 Size Effects on Boiling Curve and Peak Heat Flux 

It is also of importance to examine the heater size effect on the boiling curve. We 
plotted boiling curves for heater sizes ranging from 50 jim, 100 ^im, 270 pim, 2700 jim, 1 



i^S 



69 




(a) 



Oms 



© 




1 ms 



© 

© 


2 ms _ 



6 ms ^^^^^^ 

© 

© 


3 ms 

© 

7 ms ^^^^ 



11 ""S «^»j. 



(b) 



Figure 4.9 The visualization result of bubble departure-nucleation process for 
heater #1 at 54°C. (a) The side views; (b) The bottom views. 



70 



















/ 














^ 


y 














^ 


1 












& 


W 


M 












^? 


/* 




CoK.WISf"' , 
Colt. CCI4" 




/ 








» C«»,rvPitilin«" 
» Cola.HiOuni)'' ' 
g Hin.Wita^ 


■J 

-4 
• 










» Stnlw. Willi"" 
» SUnjttkl, Willi"' 
T aiiuiikl, UiMim'' 


1 








♦ Sl«8»(. Winr" " 
. I.I.I. 


1 - 


1 ( 










( 


f 




• Data from Yang et al. 
A The data from present 
Linear (Data from 



Yaig 



20001 
study 
et a). (20001) 



A Present study 



-2-10)2345678910 



(a) 



(b) 



Figure 4.10 The relationship between bubble departure diameter and growth time. 

(a) Experimental data and correlation curve from Yang et al. (2000); (b) Data from 

current study along with the correlation of Yang et al. (2000). 



cm to 5 cm in figure 4.11. In order to ensure a meaningful comparison, all the curves in 
figure 4.11 are based on fluids with similar thermal properties. The trend is very clear 
that as the heater size decreases, the boiling curve shifts toward higher superheats and 
higher heat fluxes. The peak heat fluxes for different size heaters have been plotted in 
figure 4.12 for comparison. It is consistent that the peak heat flux increases sharply as the 
heat size approaches the micro-scale. Actually, for heater sizes of 50 |im and 100 |im 
(Hijikata et al., 1997), even with a very high superheat of about 200°C as shown in figure 
4.11 the peak heat fluxes have not been reached. 



71 



1000 



Size effect on nucleate boiling curves 



100 



10 



>♦ 



♦ 

♦ D 



V 



♦ D 
D 




10 



-n 



♦ 50um (Hijikata et al., 1997) 
n lOOum (Hijikata et al., 1997) 
O Curretit study 

)tC2700um (Rule and Kim, 1999) 

♦ 1cm (Chang and You, 1997) 

+ 5cm (Rainey and You, 2001) 

.^ , I 



100 
Superheat(AT) 



1000 



Figure 4.1 1 Comparison of boiling curves. 



60 



50 



CHF for Different Size Heaters 



40 



r30 



X 



20 



io 



- 




270 urn 


- 




present study 

♦ 


- 




2700 urn 

♦ 


- 








♦ 


♦ 
I cm 




5 cm 





Figure 4.12 Comparison of peak heat fluxes. 



72 

4.3.3 Bubble Incipient Temperature 

Bubble incipient temperature is relatively higher for the small size heater used in 
this experiment. This is consistent with the results given by Rainey and You (2001), 
where they observed that the incipient temperature is about 16-17°C for 5 cm heater, 20- 
35°C for 2 cm heater, and 25-40°C for 1cm heater. The incipient temperature observed in 
our experiment is about 45-55°C. The explanation for this phenomenon by Rainey and 
You (2001) is that larger heaters are more likely to have more surface irregularities and 
therefore wider size range for bubble to nucleate from. 

4.3.4 Peak Heat Flux on the Microheater 

As mentioned in Section 2.3, recently more research reports (Sakashita and 
Kumada, 1993 and Sadasivan et al., 1995) have indicated their support of the macrolayer 
dryout as the basic mechanism for CHF as opposed to the hydrodynamic instabilities 
(Liehard, 1988a). In the current research with microheaters as suggested by Sadasivan et 
al. (1995), the theory of macrolayer dryout has been verified further as the cause of the 
CHF. The support based on the results of the current single bubble experiment is 
summarized as follows: 

1. As discussed in Section 4.2.3 Regimes II and III are separated by the CHF 
point. Two different mechanisms were discovered for the two regimes, respectively. It is 
clear that the CHF that is the starting point of the Regime III where the heat transfer is 
through a layer of vapor film and the heater is no longer wettable, is corresponding to the 
dryout of the macrolayer. 

2. In the current microheater condition, there is no possibility for the formation of 
Kelvin-Helmholtz instability nor Taylor instability. 



73 

4.4 Deviations from Steady Single Bubble Formation 

For the single boiling experiment dedicated in this chapter, as the bubble incipient 
temperature is reached, a steady bubbling process has been observed and analyzed as 
above. With the help of a high speed digital camera and simultaneous data acquisition, 
we have noticed some deviations from the steady single bubble bubbling process. In this 
section, these deviations have been summarized. It must be noted that these deviations 
are very random according to observations in the experiments. The physics behind these 
phenomena requires much more experimental and analytical work. We have noticed there 
are three possible phenomena associated with bubble formation that could occur. Firstly, 
a long-waiting period is necessary before the onset of another bubble and a vapor 
explosion always occurs before this onset of another bubble, we call this process 
discontinued bubble formation. Discontinued bubble formation happens usually at lower 
superheats and with a highly subcooled liquid. Secondly, the direct bubble formation is 
the process during which another bubble forms immediately after a bubble departs. 
Thirdly, the bubble jetting is a chaotic phenomenon with smaller bubbles ejected from the 
heater surface without forming a single bubble. The direct bubble formation is the steady 
bubble formation process that we have analyzed previously. This section is dedicated to 
the other two deviations from the steady bubble formation process. 
4.4.1 Discontinued Bubble Formation 

As we have observed, discontinued bubble formation actually occurs similarly to 
the initial onset of boiling on the heater. For the microheater used in out experiment, 
onset of nucleate boiling starts actually with vapor explosion, a physical event in which 
the volume of vapor phase expands at the maximum rate in a volatile liquid. During this 
process, the liquid vaporizes at high pressures and expands, performing mechanical work 



74 

on its surroundings and emitting acoustic pressure waves. According to previous 
investigators, for large heaters rapid introduction of energy is necessary to initiate and 
sustain the vapor volume growth at the high rate. For the microheater used in this 
experiment, vapor explosion always occurs prior to the nucleation of small bubbles on the 
heater. This could be due to the limited energy the microheater can supply from the solid 
surface into the liquid though the superheat is well beyond the required superheat for 
nucleating bubbles. We recorded the vapor explosion process together with the onset of 
boiling, as shown in figure 4.13 for side-view images and figure 4.15 for bottom-view 
images. When the heater reaches about 1 10°C, vapor explosion occurs. Following this 
process, small bubbles start to nucleate and coalesce almost right after. With the 
existence of noise due to the acoustic pressure waves, a layer of vapor is ejected with 
high speed up into the liquid exhibiting a shape of mushroom (about 1.0ms). The vapor 
enclosed in the mushroom is loose due to the rapid expansion, and then starts to shrink to 
form a round bubble and moves up. On top of the heater, the cool liquid replenishes the 
vacancy and small bubbles nucleate and coalesce to a single bubble. The high energy 
stored before the ONB is released suddenly to overcome all kinds of forces including the 
Van der Waals force from the solid surface, hydrostatic force due to the liquid depth, etc. 
A typical application of this process is the commercial success of thermal ink jet printers. 
The key to the thermal ink-jet technology is the action of exploding micro bubbles, which 
propel tiny ink droplets through the openings of an ink cartridge. 

Zhao et al. (1999) used a thin-film microheater of size of lOOum x UOpim to 
investigate the vapor explosion phenomenon. They placed the microheater underside of a 
layer of water and the surface temperature of the heater was rapidly raised (about 6|j,m) 



75 



ms 

-it-- 


0.5 ms'^^H 




t.Sms ^jm 





2.5 ms 






3.0 ms 



— "T « 



o 

6 



4.0 ms '*a» 







4.5 mr 



o 



5.0 ms ^^B 




5.5 ms ^H 




6.0 ms i^^V 




ms J^B 




7.0 ms Kb 





tT4 mm 



7?r 








8.5 ms 



^y 



9.0 ms 



T 







Figure 4.13 The process of vapor explosion together with onset of boiling. 



1.4 mm 



Figure 4.14 The ruler measuring the distance in figure 4.13 after vapor explosion. 



76 





1.0 ms 



ili 





2.0 ms ^^^^^^ 2.5 ms ^^^^^^ 




3.5 ms ^^ 



n 

4 



4.0 ms 



4.5 ms ,. 






ii 




''^.s 




6.0 ms 



6.5 ms 



7.0 ms 



Jfe J!5 



'fii 



7-5 ms ~W|^0 



8.0 ms 



8.5 ms 



9.0 ms 



9.5 ms 



fi^ §9 jfB fO 



; 1 , 1 «jf * 



1 1 i 1 1 1 II t^*i ■ 



Figure 4.15 The bottom images for vapor explosion and boiling onset process. 



rs 



77 

electronically well above the boiling point of water. By measuring the acoustic emission 
from an expanding volume, the dynamic growth of the vapor microlayer is reconstructed 
where a linear expansion velocity up to 17m/s was reached. Using the Rayleigh-Plesset 
equation, an absolute pressure inside the vapor volume of 7 bars was calculated from the 
data of the acoustic pressure measurement. In this experiment, we also measured the 
bubble velocity when vapor was exploded. By referring the heater size shown in figure 
4.14 the distance the bubble was ejected up from the heater surface can be measured. The 
result is the average velocity during the first 7 milliseconds is about 0.2m/s which is well 
below that measured by Zhao et al. (1999). The low velocity measured in this experiment 
is not surprising due to the following reasons. One of the reasons is that only a layer of 
water was used in their experiment while pool boiling experiment was used in this 

experiment. Also in this experiment the boiling liquid FC-72 with a lower saturation 

*>?'■ 
temperature is used. , \.J 

Figure 4.16 illustrates the heat flux traces corresponding to the vapor explosion 

and boiling onset process. In figure 4.16(a) during the 6-second data acquisition, it starts 

at a lower level where boiling is not present with natural convection to be the heat 

transfer mode. All of a sudden, the vapor explosion exists and we recorded a sharp heat 

flux spike that is supposed to correspond to the vapor explosion process as shown in 

figure 4.16(b). For present data recording speed about 4,500 data points per second, we 

recorded the vapor explosion occurs only in a mini-second related to the heat flux 

variation from the heater. Following this vapor explosion, small bubbles start to nucleate 

and heat flux increases. 



78 



FrwOOl I 1»F»b20fl2 I ' 



110 
100 



I 80 



The Heat Flux History Recording Onset of Boiling Process 



Vapor explosion and onset of boiling 



Natural convection 




^y^ 



(a) 



FramaOOl 1 »F«b3M2 1 | 




The Heat Flux History During Vapor Explosion and Onset of Boiling 




60 

^ 70 

1 " 

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40 






























































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}1 2.015 2.02 2.025 2.03 2.035 2. 

Seconds 



(b) 



Figure 4.16 The heat flux variation corresponding to the vapor-explosion and boiling 
onset process, (a) The heat flux variation recording the vapor-explosion and boiling onset 
process; (b) The heat flux variation during the vapor-explosion and boiling onset process. 



V* 

4.4.2 Bubble Jetting 



79 

During the single bubble boiling process, we observed that periodically there is 
bubble jetting after two or three bubbling cycles. This bubble jetting lasts about 0.2 
second each time before a new single bubble is formed on the heater. Images taken with 
the high speed camera in figure 4.17 and figure 4.18 show the bubble jetting process, and 
figure 4.19(a) is the heat flux traces for a six-second data acquisition which includes three 
bubble cycles of the departing-nucleation process. Figure 4.19(b) and 4.19(c) are the 
close-up views of two heat flux encircled in figure 4.19(a). Through a close observation, 
we find figure 4.19(b) is the heat flux variation corresponding to this bubble-jetting 
process shown in figure 4.17 and figure 4.18. We notice that during the bubble-jetting 
process, the heat flux stays much higher and drops sharply as a single bubble grows on 
the heater. We also observed the single bubble boiling at 105°C and 120°C. At these two 
temperatures, we also noticed the same phenomenon of bubble jetting. Figure 4.20 shows 
the heat flux variation from the heater when it is set at 105°C, and figure 4.21 shows the 
heat flux variation from the heater when it is set at 120°C. For both these two cases at 
105°C and 120°C, we also observed the bubble-jetting after bubble's departure. The 
bubble jetting process is a characteristic of chaotic bubble nucleation, merging, and 
departing process with the company of acoustic waves. During the bubble jetting process, 
small bubbles on the heater keeps merging and departing. And all of a sudden a merged 
bubble stays and merges with all other small bubbles around it, then a single bubble is 
formed. The single bubble formation and growth also inhibits the bubble-jetting process, 
and at the same time dries out the microlayer around the bubble for this particular heater 
configuration used in this experiment. Thus the heat flux drops quickly as the single 
bubble grows. The possible reason for this bubble jetting phenomenon is due to the high 



80 

superheat of the heater, the evaporation rate is very high on top of and around the edge of 
the heater. The small bubbles do not have enough liquid to replenish the microlayer 
region for them to grow. Clearer explanation of these phenomena needs further 
observation and numerical approach. 






81 




191 ms 

1 


192 tns 


• 


1 93 ms , 


194 ms . 


196 ms • 
• 




jrr 5 




fTSr- -" 'trr <a 


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Figure 4.17 The chaotic bubble jetting process for heater #1 at 110°C. 



82 



56 ms 






60 ms 





61.5 ms 




62 ms 



62,5 ms 



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67 ms 


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167.5 ms 


168 ms 


169 ms 


170 ms 


171.5 ms 




173 ms 


173.5 ms 


174 ms 


175 ms 

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176 ms 



Figure 4.18 The bottom images of chaotic bubble jetting process for heater #1 at 1 10°C. 



83 



FwtmOOI I 06F«b2M2 1 | 




Typical heat flux variation #1 at 1 10°C 




120 

110 

rf^ 100 

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1 80 

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Heat Flux Variation during Nucleation-Departing Process 













































































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Second! 



(b) 



FnmaMI 1 0>FM|2M2 1 — 1 


130 


The heat flux variation with invisible bubble jetting 


120 

110 

n-^ 100 

1 90 

1 so 

s 

Z 70 
60 
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Second* 



(c) 
Figure 4.19 The heat flux traces corresponding to the bubble jetting process, (a) 6-second 
data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view of (a) 

for direct bubble formation. 



84 



FranwMI IMF«b2002 1 | 




Typical heat flux variation #1 at 105°C 


120 

110 

.T- 100 

^ 90 

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FramaOOl 1 06 Fab 2002 | | 




Typical heat flux variaUon #1 at 105°C 


120 

110 

iQ 100 

^ 90 

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60 
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Typical heat flux variation #1 at 105°C 




120 

110 

■C 100 

? 90 
I 80 

Z 70 
60 
50 
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1-1 1.2 1.3 1 

Seconds 



(c) 

Figure 4.20 The heat flux traces for bubble jetting process from heater #1 at 105°C. (a) 6- 
second data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view 

of (a) for direct bubble formation. 



85 



Fmiw Ml lMF«k 2002 1 1 




Typical heat flux variation #1 at 120°C 


120 

110 

*- 100 

'S 90 

1 «. 

X 70 

60 

50 








































































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(a) 



FfMMOOl I 0OFM2OO2 i 



130 

120 

110 

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X 70 

go 
so 



Typical heat flux variation #1 at 120°C 







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(b) 



130 

120 

110 

iT- 100 
I 

K 

C 80 



Typical heat flux variation #1 at 120°C 



: 








































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stting 
























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(c) 

Figure 4.21 The heat flux traces for bubble jetting process from heater #1 at 120°C. (a) 6- 
second data acquisition; (b) Close-up view of (a) for visible bubble jetting; (c) Close-up view 

of (a) for direct bubble formation. 



CHAPTER 5 
DUAL BUBBLE COALESCENCE 

To obtain bubble coalescence, a single bubble was generated from heater #1, at 
the same time one more bubble was generated from another heater. In the experiment, by 
referring to figure 3.1, if the other heater is too far apart like heaters #25, #29, no matter 
how high the heater temperatures are set, the bubbles will not be large enough to coalesce 
before they depart. And if the bubbles are too close like heaters #2, #3, #4, the bubble 
coalescence will not be distinguishable because the first stage of nucleation process is so 
fast that the two bubbles coalesce right after they are nucleated. In this experiment we use 
heaters #1 1 and #12 to generate the other bubble. The purpose of selecting this two pairs 
of heaters is to obtain stable bubble coalescence and investigate how heat transfer from 
the heaters can be affected due to the interaction of the bubbles on the heaters. 

5.1 Synchronized Bubble Coalescence 

In this experiment, for heaters #1 and #11, when we set two heaters at 90°C to 

95 °C, the two bubbles depart without coalescence, and they are not syncronized. We 
increase the temperature of the two heaters to 100°C, they coalesced and was 
synchronized. For heaters #1 and #12, we observed the same situation except that the 
required stable coalescence temperature is lower, 95°C. We notice that the higher the 
heater temperature, the larger the departure size of the bubbles. This implies that to obtain 
the coalescence the departure size of the bubble has to be greater than the distance of two 
nucleation sites. And we conclude that coalescence not only enhances the heat transfer 



86 



87 

which we will see shortly, the bubbles also interact with each other by retarding or 
promoting their nucleation and growth rate. 

5.2 Dual Bubble Coalescence and Analysis 

For two configurations #1 with #11, and #1 with #12, figure 5.1 shows the heat 
flux variations from each heater when the bubbles experience coalescence with that from 
the other heater at the same temperature. Figure 5.2 shows heat flux of one typical 
ebullition cycles for each heater in two configurations. Together with visualization 
results, we observed that one ebullition bubble for coalescence includes from [A] to [F], 
where [A] to [C] is the single bubble period before coalescence. [D] corresponds to the 
bubbles coalescence moment. After this point, the newly-coalesced bubble grows till the 
departing point [F]. After this, another cycle starts. The detail is as follows: 

[A]: This point corresponds to the nucleation of the new bubble and departing of 
the old bubble. As in the single bubble boiling, the embryo left from the departed bubble 
helps the next cycle and there is a heat flux spike. 

[B], [C]: The two individual bubbles are growing and gaining in size on their 
respective heaters. The mechanism is the same as in single bubble boihng at the same 
stage. 

[D]: It corresponds to the moment when the two bubbles coalesce. There is 
another major heat flux spike due to the coalescence. When the two bubbles grow to a 
certain size where their interfaces contact each other, the two bubbles merge together and 
form a new bubble. It is suggested that this coalescence be mainly due to the effect of 
surface tension between the vapor and liquid. It is also due to the interfacial surface 
tension that makes the newly coalesced bubble sitting on the top of two heaters. Because 



88 



100 
90 
80 
70 
60 
SO 
40 
30 



Heat flux variation from #1 , when coalesce with #11 at 1 1 0°C 



J 



^J 



^ 



VJ 



VJ 



; ) 



vj 



/ 



vj 



i 



VJ 



/ I 



i 



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_1 , , , L_ 



2 4 



8 10 12 14 16 

Time {seconds) 



(a) 



100 

90 

> 80 

Ito 

I 60 

I ^^ 

40 - 

30 



20 



i 



Heat flux variation from #11, when coalesce with #1 at 1 1 0°C 



I 



VJ 



i 



VJ 




vj 



U 



vj 



V 



'■•■''■■■■■■■■■■■■■■'■■■■ ■ 



8 10 12 
Time (seconds) 



14 16 18 



(b) 



100 

90 

C 80 

i ™ 

I 60 

I 50 

X 

40 

30 

20 



Heat flux variation from 




J 



I )1 , when coalesce with #12 




atlOOX 



U 



JU 



JlJlJ 



-1 , : , , I— 



8 10 

Time (seconds) 



12 14 16 18 



100 
90 I 
•C 80 
i 70 

I 60 

I 50 
Z 
40 

30 

20 



(c) 



Heat flux variation from #12, when coalesce with #1 at 1 po°C 




j(I4MWm 



M 



\J 



^ 



u^JiK 



8 10 12 

Time (seconds) 



14 16 18 



(d) 



Figure 5.1 The heat flux variation for pair #1 with #1 1 and pair #1 and #12. (a) The heat 

flux variation for #1, when coalesce with #1 1 at 1 10°C; (b) The heat flux variation for 

#12, when coalesce with #1 at 100°C; (c) The heat flux variation for #12, when coalesce 

with #1 at 100°C; (d) The heat flux variation for #12, when coalesce with #1 at 100°C. 



89 



100 
90 

Coo 

1 70 
S 60 

r 

* 40 

30 
20 



One ebullition cycle for #1 , coalesce with #11 



[A] 



[D] 



[F] 




[e: 



Time (seconds) 



(a) 



100 

90 

|80 

^70 



150 - 
' 40 ■ 
30 - 
20 — 



One ebullition cycle for #11 , coalesce with #1 



I [A] 



[F] 



[D] 




Time (seconds) 



(b) 



100 

90 

■^80 
u 

3 60 
T» 50 



One ebullition cycle for #1 , coalesce with #12 
[A] [F] 




Time (seconds) 



(C) 




One ebullition cycle for #1 2, coalesce with #1 
[A] 

m 

[D] 







[E] 



Time (seconds) 



(d) 



Figure 5.2 The heat flux variation of one typical bubble cycle (a) and (b) for heater #1 
with #11, (c) and (d) for heater #1 with #12. 



90 

the power sources are from two single heaters, the new bubble forms an oval shape with 
its long axis in the direction of two heaters. The heaters are rewetted with liquid again 
and part of heaters is in the micro-layer region, thus resulting in the heat flux spike. To 
make it clearer the coalescence process, we take a look at the heaters arrangement in 
figure 5.3. Just before coalescence as figure 5.3(a) shows, the bubbles are sitting on their 
respective heaters. The dry area indicated by the contact line covers most of heater area. 
Only a small portion of heater area is wetted with liquid in the micro region. After 
coalescence, as figure 5.3(b) shows, a large portion of heaters is rewetted with liquid 
again, which results in high evaporation rate, thus heat flux maintains at much higher 
level. 




(a) 



Dry area 



Contact line 



I r< 



45 


14 


31 


4 lira 


30 


1 1 li--Nj 




^""^ rVl\ 


1 


3- 1 1^ 1 


^29 


>^r--n. 


/ 


10 


11 


28 



(b) 



Figure 5.3 The heater dry area before and after coalescence. 

[E]: The new bubble is growing. The heat flux tends to decrease after 
coalescence, which is due to the increase of heater dry area, as in the single bubble 
boiling. Comparing with the heat flux before coalescence, the heat flux is higher. We also 
noticed from figure 5.2 that there is a substantial heat fiux fluctuation after coalescence. 



... '.^tr" ;-***t^ ** »i.^ 



",>- *** ' <" ^v.-^ 



91 

The large volume of the coalesced bubble experiences a force unbalance that makes the 
bubble oscillate back and forth. This oscillation makes the heater dry area change, thus 
resulting in the heat transfer fluctuation. 

[F]: This corresponds to the moment when the coalesced bubble departs from the 
heater surface, and new bubbles are nucleated on the heater. There is another 
corresponding heat flux spike as discussed above. 

From the foregoing analysis and comparison with the case without coalescence, it 
is clear that during the bubble life cycle the bubble nucleation results in one major heat 
flux spike, whereas for the case with coalescence, it is obvious that there are two major 
spikes during an ebullition cycle. The first is due to the nucleation of new bubbles and the 
second is due to the coalescence of the bubbles. For the case without coalescence, the 
bubble experiences nucleation, growth, detachment, and departure stages, whereas, for 
the coalescence case, the bubbles experience nucleation, growth, coalescence, 
detachment and departure. After coalescence, the heat flux maintains at a much higher 
level than that before the coalescence. 

Figure 5.4(a) and figure 5.4(b) show the average heat flux when two heaters, 
which are set at the same temperature, generate bubbles that coalesce during the 
ebullition cycle at different temperatures. Figure 5.4(a) is for configuration #1 with #11, 
and figure 5.4(b) is for #1 with #12. These results were obtained by dividing the total 
power dissipation by the two heaters total area. We have the following observations: 

The average heat flux tends to increase with heater temperature. As temperature 
increases, due to the shorter waiting period between ebullition cycles and higher 
evaporation rate, the bubbles grow faster before they are large enough to coalesce. Thus, 



92 



Heat flux from #1 1 when #1 , #11 at different supertieats 




60 70 

Supertieat (AT) 



60 70 

Supertieat (AT) 



(a) 



60 
56 

f 

i.48 

K 

i" 

^=40 
36 
32 



Heat flux from «1 when #1 , #1 2 at different superheats 




60 
56 

f 

448 

X 

2 
■",44 



ra 

0) 

X 



40 - 

36 

32 



40 



50 



60 70 

Superheat (AT) 



Heat flux from #12, wtien#1, #12 at different supertieats 





80 



90 



40 



50 



60 70 

Superheat (AT) 



I ■ 



80 



90 



(b) 



Figure 5.4 The boiling heat flux for the two pairs (#1 with #11) and (#1 with #12) as they 
are set at different temperatures to generate bubbles and coalesce, (a) The pair #1 with 

#11; (b) The pair #1 with #12. 



they coalesce earlier to allow longer time of higher heat flux during one bubble ebullition 
cycle. 

There are deflective heat fluxes at AT = 55°C for both heaters in configuration #1 

with #11, and AT = 50°C for #1 while AT = 65°C for #12 in configuration #1 with #12. 



93 

Close observation of heat flux variations in figure 5.1 for different temperatures, we 
found that the sudden drop of average heat flux is because the dryout area is larger so that 
the heat flux valley point before coalescence is lower and makes the average heat flux 
lower. 

We also noticed that for configuration #1 with #12, the deflective heat flux is not 
as apparent as #1 with #11, and occurs at different temperatures. Because #1 and #12 
have shorter distance than that for #1 with #11, they coalesce much more stably. On the 
other hand, different surface areas for #1 and #12 probably are the reasons for different 
temperatures when deflective heat flux occurs. Heater #12 (0.0748mm^) has a larger area 
than #1 (0.073 16mm^), while #1 and #1 1 (0.0732mm^) are much closer in surface areas. 
5.3 Heat Transfer Enhancement due to Coalescence 

To quantitatively compare the heat transfer between the single bubble boiling and 
dual bubble boiling with coalescence, we use the same method to obtain the average heat 
flux for single bubble boiling at the same boiling conditions. Figure 5.5 shows the heat 
transfer enhancement for the two configurations, in which figure 5.5(a) is for heater #1 
with #11 and figure 5.5(b) is for the configuration #1 with #12. For configuration #1 
with #11, the heat transfer enhancement changes substantially with the temperatures of 
two heaters, while for #1 with #12, the heat transfer enhancement is relatively stable 
within the temperatures of interest. 

Comparing the heat transfer characteristics during coalescence with those for the 
single bubble case, we offer the following summary and conclusions: 

1. There are two major heat flux spikes for the case with coalescence as compared 
to only one single major spike for the non-coalescence case. Through a quantitative 
analysis, coalescence results in a heat transfer enhancement. 



20 



16 



; 12 



4 - 



°40 



20 



16 



12 



"40 



94 



Average heat flux Increase from #1 , #11 




0.6 



0.4 



0.2 



50 



60 70 

Supertieat (AT) 



80 



90 



°°40 



(a) 



Average heat flux increase from #1 , #1 2 



5 . Heat flux percent (%) Increase from #1 , #1 2 




ninl 
run 2 

run 3 
average 



I 0.4 



0.2 



50 



60 70 

Supertieat (AT) 



80 



90 



°°40 



Heat flux percent (%) Increase from #1 , «1 1 




50 



60 70 

Superheat (AT) 



80 



90 




runi 
run 2 
runs 
average 



50 



60 70 

Superheat (AT) 



_i_ 



80 



90 



(b) 



Figure 5.5 The heat flux increase due to coalescence, (a) The pair #1 with #1 1; (b) The 

pair #1 with #12. 



2. The bubble departure frequency increases due to coalescence of bubbles by 
comparing with the single bubble case at the same boiling condition. 

3. The heat transfer from the heaters is closely associated with the bubble contact 
line movement and dry area on the heater surface. 



95 

4. We also suggest that the interfacial surface force is the determinant factor to 
render the bubbles coalescence. 

5. Degree of heat transfer enhancement depends on the configuration and 
temperature of two heaters. 

5.4 Bubble Departure Frequency 
Figure 5.6 is plotted to compare the bubble departure frequencies for the 
coalescence case with that without coalescence. It illustrates the heat flux variation 
during a 10-second period, which also indicates the bubble life cycles for the single 
bubble case and the bubble-bubble coalescence case. It is clear that when two bubbles 
coalesce, the departure frequency increases as a result of enhanced heat transfer. 



100 E- 

9o| 

80 

E 70 
u 
> 60 

^ 50 

r 40 

n 
i 30 

20 

10 





k 



/ 



.'^^-, 



J \ J |il 



J 



J J 



_..' ^^-.__ 

#1 at 110°C, coalesce with #11 
#1 at 11 0°C, without coalescence 



4 6 

Time (seconds) 



10 



Figure 5.6. Comparison of bubble departure frequency from heater #1 for coalescence 

and non-coalescence cases. 



CHAPTER 6 
HEAT TRANSFER EFFECTS OF COALESCENCE OF BUBBLES FROM VARIOUS 

SITE DISTRIBUTIONS 

6.1 Coalescence of Dual Bubbles with a Moderate Separation Distance - A Typical 

Case 

The relative locations of the two heaters #11 and #13 are depicted in figure 3.1. 
The distance between the centers of the two heaters is about the size of two heaters, i.e. 
0.56mm. When the two heaters were set at 100°C, we obtained stable bubble 
coalescence. The visualization results are shown in figure 6.1 and figure 6.2, where figure 
6.1 provides the departure and nucleation process and figure 6.2 covers the coalescence 
process. In each figure, both the bottom images and side images have been given. We can 
conclude that a typical ebullition cycle is characterized by the following stages: 
nucleation, single bubble growth, coalescence, continued growth of the coalesced bubble, 
and departure of the coalesced bubble. Also these stages have been clearly shown in heat 
flux traces plotted in figure 6.3. 

Bubble departure and nucleation process. According to figure 6.1, the bubble 
departure and the ensuing bubble embryo formation are virtually a continuous process. 
The succeeding bubble nucleation is taking place while the proceeding bubble is leaving 
the heater surface. As a bubble grows large enough in size, the buoyancy force lifts the 
bubble so that the contact line shrinks (this is visible from the bottom images). The 
surface tension force from the heater surface that is part of the forces responsible for 
holding the bubble in place decreases accordingly so that the bubble moves horizontally 
to one heater. As this happens, the other heater is rewetted and the first bubble nucleation 

96 



97 

begins as shown at 4 ms in figure 6.1. This horizontal move promotes one bubble's 
nucleation and inhibits the other bubble's nucleation, thus resulting in a time delay for the 
nucleation of the second bubble. At 6 ms the coalesced bubble departs, and the second 
bubble is nucleated at 7 ms. Therefore, there is about a 3 ms delay between the nucleation 
of the two bubbles. The heat flux history given in figure 6.3 shows there is a heat flux 
spike associated with this process. Just prior to this heat flux spike due to departure and 
nucleation, we noticed that the heat flux exhibits wave-like fluctuations with a period 
about 0.42 ms. These fluctuations as observed are due to the size oscillation of the 
coalesced bubble. After the departure/nucleation heat flux spike, the heat flux drops 
sharply as the new bubbles grow. This heat flux drop is a direct result of bubble growth 
that produces more dry area on the heater surface. As seen in figure 6.3(b), we found that 
it takes about 0.01 second for the heat flux to decay to the lower level. After this, the heat 
flux still drops as the bubble grows, but the drop rate is much slower. During the slow 
growth period, conduction through the vapor is the main heat transfer mechanism. 

Bubble coalescence process. As the bubbles grow large enough to touch each 
other, they coalesce. The coalescence process starts with the touching of the interface of 
the two bubbles, shown in figure 6.2 (at 163 ms). At the next millisecond (164 ms), the 
common area of the liquid-vapor interface of the two bubbles ruptured, thus resulting in a 
strong surface tension force acting on the ruptured area. Figure 6.4 is used to illustrate 
this point. Before the rupture of the interface of the bubble, the surface tension keeps the 
bubble as it is. After rupture, the peripheral of the rupture area is occupied by the 
remaining surface tension, and this force pulls the rupture area of the bubble outward. 
And this pulling draws the bubble toward each other with a large initial speed. This 



98 

inertia makes the new bubble oscillates several cycles (about 4 to 5 cycles) before it 
settles into its final shape. Each time it stretches, some energy is dissipated; thus the 
strength lessens after each stretch. The first stretch is the strongest. The bubble is pulled 
in oval shape with the major axis perpendicular to centerline of the two heaters, thus 
resulting in the minimum dry area on the two heaters as shown in figure 6.4. This point 
should be responsible for the heat flux peak during the merging process as shown in 
figure 6.3(b). As we have observed, this heat flux peak is not attributed to the interface 
interaction when the two bubbles touch because at this moment, the bubbles themselves 
are still held at their original place, thus the dry areas have not been changed 
substantially. Before the new bubble settles, its size oscillates several cycles. These 
oscillatory motions lead to the secondary heat flux spikes following the first heat flux 
spike. In figure 6.3(c), there are five heat flux spikes that correspond to the five 
oscillations during the bubble coalescence process. The dry area variation during the 
coalescence process has been shown in figure 6.2(b). Figure 6.4(b) corresponds to the 
image at time 164 ms in figure 6.2(a) when the interface area ruptures. Figure 6.4(c) 
corresponds to the minimum dry area at time 167 ms in figure 6.2(a) at the time of the 
first and largest spike. We also observed from the images in figure 6.2(a) that the 
coalescence results in higher convection heat transfer, and natural convection heat 
transfer around the bubbles due to the subcooled liquid used in this experiment. 



99 




Q^uji44l 




(a) 



Oms '* 



Ims '* 



2m» * 



3ms 



o o .o o 



5ms 



6 ms 



7 ms 



m 



•O ^ 9 « O ' O 



8m» '« 



9nw > 



10 ms ■» 



lima ^ 



o © .© .© 



(b) 

Figure 6.1 The departing and nucleation process for heaters #1 1 and #13 at 100°C. (a) 

The side views; (b) The bottom views. 



100 




(a) 



163 ms* 164 mS* 

.•8* .-8* 

167ntt%. I 168m«i 


165 ms' 

.0- 


166 ms' . 4 

..rv 

170 ms« 

174 msV 1 


169 ms« 

173m8'^ 1 


171 ms' 172 ms< 



(b) 



Figure 6.2 The coalescence process (2 cycles of oscillation) for heaters #1 1 and #13 at 
100°C. (a) The side views; (b) The bottom views. 



101 



130 
120 
110 
100 
90 
80 
70 
60 
50 
40 
30 



Heat Hux for heater #1 1 when #1 1 and #13 both at 100°C 



departure-nucleation Coalescence process 

process 




\|H*I^' 




seconds 



(a) 



Heat flux variation during departure-nucleation-coalescence process 
Departing! 

Coal escence process 




(b) 



Heat flux variation during coalescence process 




(C) 



Figure 6.3 The heat flux history for dual bubble coalescence, (a) 6-second data 

acquisition of heat fluxes including 5 cycles; (b) Close-up heat flux variation from (a) for 

one typical ebullition process; (c) Close-up heat flux variation from (b) for coalescence 

process. 



102 



Bubble shape after first stretch 



Bubble shape just before coalescence 





Surface 
tension 




(a) 




(b) 




(c) 



Figure 6.4 Photographs showing the interface interaction, (a) Schematic showing the 
coalescence procedure; (b) Two touching bubbles; (c) The coalesced bubble. 



103 



6.2 Dual Bubble Coalescence from Heaters #11 and #14 at 100°C - Larger 

Separation Distance Case 

The relative locations of the two heaters #11 and #14 are given in figure 3.1. The 
distance between the centers of the two heaters is about three-heater size, i.e. 0.84 mm. 
When the two heaters are set at 100°C, we can obtain stable bubble coalescence. Unlike 
the case for heaters #1 1 and #13, from the images shown in figure 6.5 and figure 6.6, we 
found that a typical ebullition cycle is characterized by different stages: nucleation, single 
bubble growth, coalescence, and departure. Comparing with the cycle of heaters #11 and 
#13 both held at 100°C, the stage of continued growth after coalescence is absent. 
Instead, the coalesced bubble departs right after they coalesced. These stages can be seen 
from the visualization results provided in figure 6.5 and figure 6.6, and also have been 
clearly shown in the heat flux traces plotted in figure 6.7. 

The main reason for the immediate departure after coalescence comes from the 
balance between the lifting force and the holding force of a sessile bubble. The lifting 
force is basically the buoyancy force that is proportional to the volume of the bubble, 
while the holding force consists of contact pressure, hydrodynamic pressure, drag and 
surface tension. The holding force is dominated by the contact pressure and the drag 
force which are proportional to the square of the radius. As the ratio of the lifting force to 
the holding force is proportional to the radius of the bubble, the radius of a bubble must 
be greater than the critical radius for the buoyancy force to over-power the holding force 
to lift the bubble. For the case of #11 and #14 coalescence, the two individual bubbles 
grow to larger sizes before they touch each other and coalesce because of the larger 
heater separation distance. Therefore the radius of the coalesced bubble in the #1 1 and 



104 




W JHI!^E'l 




Figure 6.5 The side-view photographs of coalescence-departure-nucleation process 

for heaters #1 1 and #14 at 100°C. 



¥ 




105 



T" — — T- r- 1- 'C- 13 

1 ms ^^^_ 2 ms .. 3 ms ' 



A 



■Ml. 






5 ms ' 6 ms 







9m8 '10 ms ' llms 

4^ ••O -^ €► 



12 ms 13 ms 14 ms 15 ms 

^ .4^ .0 



17 ms , 18 ms 19 ms 



21 ms ' r 22ms ^ ] 23 ms '^ T 

^ O O -^ 



Figure 6.6 The bottom view of coalescence-departure-nucleation process 
for heaters #1 Iwith #14 at 100°C. 



106 







c 






m 


■■ 




110 


r 


rP 


100 


■- 






90 


;. 












1 


BO 


- 












X 


70 


- 




3 








C 


60 


— 












? 




_ 




« 






1 


X 


40 
30 


- 


I 




- 




20 


- 




to 


, 



a 

X 



Heat flux for heater #1 1 when #1 1 and #14 both at 100°C 
Coalescence and departing process 



L^ 



J ^''^-'— JUJw. 



Seconds 



(a) 



Heat flux for variation for#l 1 during departing and coalescence process 




Seconds 



(b) 



Figure 6.7 The heat flux history from heater #1 1 when #1 1 and #14 are set at 100°C. (a) 
6-second data acquisition of heat fluxes from #1 1 ; (b) Close-up heat flux variation at 

coalescence-departing process. 



#14 case is greater than the critical radius which facilitates the immediate departure while 
for the case of #11 and #13, the radius of the coalesced bubble is below the critical 
radius, thus it needs to grow further before departure. 

The heat transfer enhancement from coalescence is due to the following 
mechanisms: (1) The bubble departure frequency increases because the bubble departs 
right after coalescence. For single bubble boiling, one bubbling cycle takes about 2 



107 

seconds, while for this case, due to the coalescence, one bubbling cycle takes about 1 

second. This can be seen in both figure 6.5 and figure 6.6. (2) The coalescing process 

promotes other transfer modes such as the convection and conduction heat transfer. 

The heat flux history shown in figure 6.7 carries some similarity to that from 

single bubble boiling without coalescence. But some important aspects have 

distinguished them from each other. Firstly, the bubbling cycle frequency is almost 

doubled for the coalescence case, which definitely enhances the heat transfer. Secondly, 

the departure mechanism for the coalesced bubble is different from that for the single 

bubble boiling. From the heat flux history in figure 6.7(b), we can see, due to 

coalescence, that the bubble departure from each heater is pretty straightforward. But for 

the single bubble case, the bubble always experiences some heat flux fluctuation before 

the buoyancy force lifts the bubble from the heater. 

6.3 Dual Bubble Coalescence from Heaters #11 and #14 at 130°C - Larger 
Separation Distance and Higher Heater Temperature Case 

When the two heaters are set at 130°C, we can also obtain stable bubble 

coalescence. Due to an increased temperature from 100°C to 130°C, the bubbles exhibit 

different behavior. The heat flux history corresponding to each stage has been shown in 

figure 6.8. We can see one typical ebullition cycle is characterized by the following 

different stages: nucleation, single bubble growth, coalescence, short growth and 

departure. In this case, the bubbles experience almost the same stages as those of the case 

for #11 with #14 at 100°C. The only difference is that due to the different heater 

temperature, the coalesced bubble did not depart right after coalescence. Instead, the 

coalesced bubble oscillated few cycles and then departed, which is different from the 



108 




Heat flux variation for #1 1 when #1 1 and #14 botli at 130°C 



^--^^ 




VU 



(a) 



Heat flux variation during departing and coalescence process 




(b) 

Figure 6.8 The heat flux history for heaters #1 1 and #14 at 130°C. (a) 6-second data 

acquisition of heat fluxes from #1 1; (b) Close-up heat flux variation from heater #1 1 

during coalescence and departing process. 



after-coalescence slow growth observed for the case of coalescence from #11 and #13. 
This difference can be further illustrated by figure 6.3 and figure 6.8. The reason that the 
coalesced bubble did not depart immediately is thought due to the effect of temperature 
on the densities of the FC-72 boiling fluid. As a result of the heater temperature increase 
from 100°C to 130°C, the buoyancy force is reduced by 15% accordingly as the Uquid 
density decreases with temperature while the vapor density increase with temperature. 



109 

6.4 History of Time-resolved Heat Flux for Different Heater Separations 

Next, we focus on the effects of the separation distance between the heaters. 
Three cases were performed where heater #1 with heater #4 (0.281 mm), heater #1 with 
heater #13 (0.541 mm), and heater #1 with heater #11 (0.770 mm) were investigated. 
Figure 6.9 shows the time resolved heat fluxes for the three cases. Figure 6.10 shows the 
corresponding images taken from the bottom of the heaters. In our previous work (Chen 
and Chung 2002), we found that in general there are two heat flux spikes in the 
coalescence of two identical bubbles. One is due to the combined process of departure 
and nucleation, and the other one is due to the coalescence. From figure 6.9 and figure 
6.10, we have the following observations: For the shortest separation distance (0.281 
mm) among the three cases, there is only one clear spike for each boiling cycle which is 
definitely due to the bubble departure/nucleation process. There is no apparent 
coalescence observed either from the heat flux measurement or visualized images. It is 
believed that simply there is no room for two individual bubbles to develop. From the 
time-resolved heat flux traces where the heat flux fluctuates very much indicates that the 
bubble experiences significant vibration over the heaters. At the separation distances of 
0.451 mm and 0.770 mm, coalescence of bubbles can be clearly observed both from the 
heat flux trace and the visualized images. Also obviously, at the shorter distance of 0.451 
mm, bubbles coalesce earlier than that at the longer distance of 0.770 mm during a 
bubbling cycle. As explained before, this phenomenon is due to the fact that bubbles 
touch each other earlier for the shorter separation distance case. 

6.5 Time Period of a Bubbling Cycle 
It is interesting to study the periods of bubbling cycles for heater pairs with 
different separation distances. Usually we found that the longer the period the lower the 



no 



110 

100 

^ 90 

I ^ 

§ 60 

S 50 
CO 

X 40 



30 

20 - 
10, 



Heat flux with time from heater #1 , when t)oth #1 and #4 at 11 0°C 




Heat flux with time from heater #1 , when both #1 and #1 3 at 1 1 0°C 




Time (seconds) 



(b) 



Heat flux with time from heater #1 , when both #1 and #1 1 at 1 1 0°C 




Time (seconds) 



(C) 

Figure 6.9. The heat flux history from heater #1 with time, (a) Heat flux from #1 with 

time when #1 and #4 are set at 1 10°C; (b) Heat flux from #1 with time when #1 and #13 

are set at 1 10°C; (c) Heat flux from #1 with time when #1 and #1 1 are set at 1 10°C. 



Ill 




(a) 




(b) 




(c) 



Figure 6.10 The bottom images for one bubble cycle and dryout changing (time in 

second), (a) One bubbling cycle for #1 with #4 set at 1 10°C; (b) One bubbling cycle for 

#1 with #13 set at 1 10°C; (c) One bubbling cycle for #1 and #1 1 set at 1 10°C. 



112 

average heat fluxes. Figure 6. 1 1 shows the time period of a bubbling cycle as a function 
of the heater superheat for five pairs of heater arrangement. These five pairs represent a 
range of heater separation distance between 0.280 mm to 0.770 mm. There is a common 
trend for the period curves among all pairs. For each heater pair, the period of the 
bubbling cycle initially increases until the superheat reaches to 45°C ~ 50°C, then it 
decreases monotonously. This phenomenon can be explained by the competition between 
two mechanisms. It should be pointed out that every bubbling cycle ends with the 
departure of a single bubble if no coalescence occurs or the departure of the coalesced 
bubble. Therefore the earlier the bubble departs the shorter the period is. For a given pair 
of heaters, as the temperature of the heaters is increased, the buoyancy force decreases as 
explained before, which is the mechanism that retards the bubble departure. While on the 



1-8 I- 



1.6 



Time duration of one coalescence cycle 



? 14 

1 

•« 1 2 
^1.2 

I 1 

s 
ja 

S 0.8 

o 

■s 

I 0.6 
C 

3 

I 0.4 



0.2 - 




-A with #4, at 0.280 mm 

-▼ with #3, at 0.385 mm 

-•< with #13, at 0.541 mm 

-♦ with #12, at 0.609 mm 

-• with #4, at 0.770 mm 



O'l I I I I I I I I I I I I I I I I r I I I I I I I I I I I I ,, I I I , , 

30 40 50 60 70 80 90 100 

Superheat (AT) 



110 



Figure 6.1 1 The time duration of one bubble cycle at different superheats. 



> \ 






^t"" 



113 

other hand, we anticipate that the higher the heater temperature the higher the heat 
transfer to the bubble which causes the bubble to grow faster and therefore promotes 
bubble departure. We suggest that the retarding mechanism prevails before the peak 
period and after that the promoting mechanism dominates. At a given heater superheat, 
the longer the separation distance is between the heaters, the shorter the period of 
bubbling cycle is measured. This is explained by the larger rewetted area and higher 
induced convection due to more violent coalescence when the two heaters are separated 
at a larger distance. 

6.6 Average Heat Flux of a Heater Pair - Effects of Separation Distance 
As discussed in the above, the two-phase condition on one heater of a heater pair 
during the coalescence experiment is not identical to that of the other heater. From 
practical point of view, it is useful to examine the average heat flux for a given pair of 
heaters at various superheats. Figure 6.12 shows the average heat flux of a boiling cycle 
for seven heater pairs with the separation distance ranging from 0.280 mm to 0.810 mm. 
These data were derived by dividing the sum of the two heat transfer rates over the total 
area of two heaters. The results are relatively very consistent which show the heat flux 
increasing linearly with the superheat. For a given superheat, the heat flux increases with 
increasing separation distance. With a larger separation distance, more of an individual 
heater surface would be rewetted by the surrounding liquid that facilitates higher heat 
transfer rates. 

6.7 Time-averaged Heat Flux from Heater #1 
Figure 6.13 is used to illustrate the effects of heater pair configuration on the heat 
transfer. Here heater #1 is chosen as the reference heater and therefore, in figure 6.13, the 



114 



70 



60 



^ 50 
t 40 



» 30 



Average heat flux from dual heaters with different distances 



20 - 



10 - 




#1 with #4 -- 0.280mm 

•T #1 with #3 -- 0.385mm 

♦ #1 with #13 --0.541mm 

t #1 1 with #13 - 0.546mm 

« #1 with #1 2 - 0.609mm 

♦ #1 with #1 1 - 0.770mm 

« #11 with #14 -0.810mm 



r I I I I — i_i — I — \ — I I I I I I I I L-i I I i_i I I ' ' ' ' ' ' ' ' ' 

30 40 50 60 70 80 90 

Superheat (AT) 



Figure 6.12 The average heat fluxes from different pairs of heaters at different 

superheats. 



70 



60 



^ 50 

CM 

E 

*, 40 

X 

3 



30 



«> 

X 



20 



10 



Average heat flux from heater #1 
- when coalesce with different heaters at different distances 




^ with #4, at 0.280mm 

"W with #3, at 0.385mm 

♦ with #13, at 0.541 mm 

• with #12, at 0.609mm 

m with #11, at 0.770mm 



qI I I I 
30 



40 







50 



60 70 80 

Superheat (AT) 



90 



100 



Figure 6.13 The average heat fluxes from heater #1 at different superheats. 



115 

time-averaged heat flux of this heater is plotted as a function of the heater superheat for 
five cases where the second heater is placed at various positions relative to heater #1. In 
general, figure 6.13 is very similar to figure 6.12, which means that the time averaged 
heat fluxes from the two heaters are very close to each other. 

6.8 Coalescence of Multiple Bubbles 

In this experiment, we use four different heater configurations to perform multiple 

bubble coalescence: A. triangle - three bubbles from #1, #12, and #14, B. tight square - 

four bubbles from #1, #2, #3 and #4, C. loose square plus center - five bubbles from #1, 

#15, #3, #5 and #7 and D. loose square - four bubble from #15, #3, #5 and #7. Figure 



17 


36 


35 


34 


33 


18 


5 


16 


15 


14 


19 


6 


1 


4 


13 


20 


7 


2 


3 


12 


21 


8 


9 


10 


11 



17 


36 


35 


34 


33 


18 


5 


16 


15 


14 


19 


6 


1 


4 


13 


20 


7 


2 


3 


12 


21 


8 


9 


10 


11 



Case A: three heaters 1-12-13 



Case B: four heaters 1-2-3-4 



17 


36 


35 


34 


33 


18 


5 


16 


15 


14 


19 


6 


1 


4 


13 


20 


7 


2 


3 


12 


21 


8 


9 


10 


11 



17 


36 


35 


34 


33 


18 


5 


16 


15 


14 


19 


6 


1 


4 


13 


20 


7 


2 


3 


12 


21 


8 


9 


10 


11 



Case C: five heaters 1-3-5-7-15 



Case D: Four heaters 3-5-7-15 



Figure 6.14 Four heater configurations for multiple bubble coalescence experiment. 



116 



6.14 provides the schematic of these four cases, where the selected heaters were 
highlighted for each case. For the multibubble experiment, the heaters were all kept at the 
same temperature during each run. The heater temperature was varied with superheats 
ranging from 34°C to 84°C in 5°C increments. For each superheat, the heaters were set 
and maintained at that temperature. The detailed coalescence process recorded by a high 
speed camera was obtained for visualization. 

Average heat fluxes of individual heaters vs. superheat. First we present time- 
averaged heat fluxes for Case A - three-bubble coalescence in figure 6.15. The same 
experiment was repeated three times and the results show an excellent repeatability. In 
general, the heat fluxes increase monotonically with the superheat for all three heaters. 
Concerning the individual heaters, heat fluxes from #12 and #14 are supposed to be 
identical to each other because of geometric symmetry. In reality, the level of heat flux 
depends strongly on where the coalesced bubble is located which determines the rewetted 
and dry area ratio for a particular heater. For the results given in figure 6.15, it is apparent 
that the coalesced bubble is located closer to #12. The reason for which the coalesced 
bubble is located near #12 is given later in the section of visualization. To further 
demonstrate the relationship between the heat flux level and the location of coalesced 
bubble, we present figure 6.16 where the time-averaged heat fluxes are plotted for all five 
heaters for Case C - loose square with center. For Case C, the coalesced bubble 
inevitably is located near the center heater # 1 which also turned out to have not only the 
lowest but substantially lower heat flux level than those of the four comer heaters. This 
finding is consistent with that reported by Rule and Kim (1999), where 96 heaters in a 10 



f',^ 



117 

X 10 square array have been used in pool boiling experiment and they found that the 
surrounding heaters exhibit higher heat fluxes than those from the inner heaters. 



70 



60 - 



g 55 
p 



0> 

I 45 



40 - 



30. 



- 


Heat flux from each heater when #1, #11, #12 are set 




L 


at different superheats 




; 


^^^^^^"♦— •— ^ 


>^^ 


- 


y^l^Z/^ ^^^^^^*===-><r»"""*^^ 


J^^^^"'^ 


- 


y^ 




- 


/^^^=<T 




" 


^n*"-'^^'''*^ *— 


- #1 Run3 




cy''"^^ — * — 


- #12Run1 


- 


0— 


- #12Run2 


" 


— o— 


- #12Run3 








. 


' 




- 


D — 


- #14Run3 









30 



50 60 70 

Superheat (AT) 



Figure 6.15 The heat fluxes from each heater for case A (figure 6.14) vs. superheat. 




<1 Runi 
f 1 Run2 
(1 Runs 
(15 Runi 
<15Run2 
• 1SRun3 
«3Runl 
tSRunl 
•3 Runs 
tSRunI 
•5a|in2 
•SRunS 
•7 Runi 
•7Run2 
-e »7RunS 

0' I ' I ' I ''''''''''''''*'''' I'''' I'''' ' 
20 30 40 50 60 70 80 90 



superheat (AT) 



Figure 6.16 The heat fluxes from each heater for case C (figure 6.14) vs. superheat. 



118 

Comparison of heat transfer enhancement from various multibubble 
coalescence configurations. For the purpose of quantitatively evaluating the 
multibubble coalescence effects on boiling heat transfer, we have selected six 
configurations : Cases A, B, C, and D defined above together with Case E - heaters #1 
and #3 and Case F - heaters #1 and #13. Cases E and F provide the base cases for 
coalescence of twin bubbles. The summary of the results is plotted in figure 6.17 where 
each curve represents the averaged heat flux for a particular set of heaters as a function of 
the superheat. The heat flux levels in descending order are D, A, C, F, E, and B. Let us 
first focus on Cases D, A, and F as they represent four-bubble, three-bubble and two- 
bubble coalescences, respectively, with approximately equal separation distances 
between any two heaters. As discussed earlier, the separation distance is an important 
parameter because it determines the portion of rewetted area on a heater. With the 



70 



60 



50 

E 
u 
^ 40 

X 

_3 

■5 30 

0) 

X 



20 



10 - 



Average heat flux for different configurations 
vs. superheat 




30 



40 



1-3 Case E 
1-13 CaseF 
1-12-14 Case A 
1-2-3-4 CaseB 
1-3-5-7-15 CaseC 
3-5-7-15 CaseD 



50 



60 
Superheat (AT) 



I I I I— I I— I—I I L 



70 



80 



Figure 6.17 The average heat fluxes for different heater configurations vs. superheat. 



' 119 

separation distance removed as a factor, we may conclude that the more bubbles 
participate in the formation of a single coalesced bubble, the higher the average heat flux 
level would result among the heaters involved. The reason that the enhancement is 
proportional to the number of bubbles is thought due to that the number of individual 
coalescences before the formation of a single coalesced bubble increases with increasing 
number of participating bubbles. For the rest of cases, the reason that Case C results in 
higher heat fluxes than Case E is also due to more bubbles participating in coalescence 
for Case C than for Case E. Case B has shortest distances among heaters, thus lowest heat 
flux levels. The reason is mainly due to the lack of room for coalescence resulting in 
virtually no rewetting and little induced convection. 

Flow visualization of coalescence meclianisni. We selected Cases C and D for 
the flow visualization study. The images were obtained for the bottom view of the 
heaters. The basic difference between the two cases is that the average separation 
distance for Case D is larger because it does not have the center heater. Figures 6.18 and 
6.19 provide the coalescence sequence for both cases at a heater superheat of 80°C. In 
general, the bubble that departs eventually is a product of multistage coalescences. 
During each stage, there is a single coalescence between two adjacent bubbles. For 
example in Case D (figure 6.18), the two bubbles on the right-hand-side merge first, then 
the coalesced bubble from the first stage merges with the lower one on the left-hand-side, 
after that the coalesced bubble from the second stage merges with the left upper one to 
complete the third stage of coalescence. After the third coalescence, the combined overall 
bubble departs. It is noted that by the time the overall bubble departed, the next 



120 



ms ^,-._ iSTms 1 .5 ma 3.5 ms 



5.5 m! 




7.5 IDS 




; 9.5 ms 



11.5 mSi 






Figure 6.18 The coalescence sequence for heaters #3, #5, #7, and #15 at 80°C. 



Oms 




0.5 




3.5 ms 




Jln^, 




26.5 ms 37.5 ms 



40.5 




108.6 




MiOms 



156.5 






Ik- 




241ms 242ma^j 



Figure 6.19 The coalescence sequence for heaters #1, #3, #5, #7, and #15 at 80°C. 



121 

generation bubbles have already grown to medium sizes. The main reason for the 
multistage process is that all the bubbles would be at somewhat slightly different sizes at 
any instant, therefore, they do not touch one another at the same time. Whenever any pair 
that grows closer enough would coalesce first. For Case C (figure 6.19), the coalescence 
mechanism is similar, but with the extra bubble in the center, there are four stages rather 
than three as in Case D. Based on figures 6.18 and 6.19, we may conclude that for Case D 
with a larger separation distance, the overall bubble departs much quicker and thus it 
results in a shorter cycle period. Also the size of the overall bubble is smaller for Case D 
which gives rise to larger rewetted area. The combination of a shorter cycle and more 
rewetted area is believed to be responsible for the higher time-averaged heat flux shown 
in figure 6.17. Figures 6.20 and 6.21 show the coalescence sequences for Cases C and D 
at a superheat of 100°C. At a higher superheat, the coalescence mechanism remains 
similar to that of the lower superheat. The major differences are that the pace is faster and 
the overall bubble size is larger. 




Figure 6.20 The coalesced bubble formed on heaters #3, #5, #7, and #15 at 100°C. 




Figure 6.21 The coalesced bubble formed on heaters #1, #3, #5, #7, and #15 at 100°C. 



122 

6.9 Heat Transfer Enhancement due to Coalescence Induced Rewetting 

In Chen and Chung (2002) and in previous sections of this paper, we have 
attributed higher heat transfer rates to the coalescence-induced rewetting of a heater 
surface. In this section, we have designed an experiment to further clarify this heat 
transfer enhancement phenomenon. Two heater configurations have been used to 
compare the heat fluxes. The first one is composed of #1, #2, #3, #4 and #11 heaters. 
The second one is composed of just #3 and #1 1 heaters. For all the results obtained, #1 1 
heater was always kept at 80°C, while for the first configuration #1, #2, #3 and #4 have 
been allowed to vary with superheats ranging from 25°C to 80°C. The same superheat 
range was applied to #3 heater in the second configuration for all the experimental runs. 
As a result of the above settings, the heat flux registered on the #1 1 heater will provide an 
unbiased comparison because it is kept at a single temperature at all times. The time- 
averaged heat fluxes of #11 heater are plotted in figure 6.22 for both heater 
configurations. For each configuration, three runs were performed to ensure the 
repeatability. It is clear that the heat flux level for the first configuration is approximately 
20% higher than that of the second configuration. For the first configuration, heaters #1, 
#2, #3 and #4 always produce a single but larger bubble as shown in figure 6.23. The 
bubble produced by the #11 heater is smaller and therefore is absorbed by the larger 
bubble on heaters #1, #2, #3 and #4 as seen in figure 6.23 which results in a rewetting of 
the entire surface on the #11 heater. While for the second configuration, bubbles 
produced on heaters #3 and #11, respectively, are roughly equal in size and the coalesced 
bubble is located in the middle between the two heaters which results in only a partial 
rewetting of the #1 1 heater. Figure 6.24 is a plot of the heat flux history for #1 1 heater. 



123 



70 



60 



50 



I 40 

X 



■a 30 



20 - 



10 - 



Heat flux from #1 1 at 80°C 




Run1 -#1 ,#2,#3,#4 at various superheats 
Run2-#1 ,#2,#3,#4 at various supertieats 
Run3-#1,#2,#3,#4 at various supertieats 
Run1-only#3 at various supertieats 
Run2- only #3 at various superheats 
Run3- only #3 at various superheats 



I I ' I I I I I ''''''''''''■'' I '■' I'' ' 
30 40 50 60 70 80 

Superheat(AT) 



Figure 6.22 The heat fluxes from heater #1 1 when the other heaters are at various 

superheats. 




Figure 6.23 The heat flux history from heater #1 1 during 0.8 second. 



124 



Heat flux from #1 1 at 80°C with time 




Figure 6.24 The heat flux history from heater #1 1 when the bubble formed on it is pulled 
toward the primary bubble from heaters #1, #2, #3, and #4. 



The history shows a mixture of short and long cycles, approximately a long cycle is 
followed by three short cycles. Each spike in the short cycle corresponds to the rewetting 
of the heater surface as the bubble is absorbed by the larger bubble. The long cycle is 
produced due to growing of the larger bubble on heaters #1, #2, #3 and #4. After the 
departure of the larger bubble, the smaller bubble on heater #1 1 would stay longer on the 
heater and grow slowly waiting for the larger bubble to grow to the appropriate size for 
merging. In other words, the large bubble would absorb three small bubbles before 
departure. 

Based on the experimental work and analysis given in this chapter, some 
conclusions can be drawn in the following. 

An experimental work has been performed to investigate the heat transfer 
enhancement from the coalescence of multiple bubbles at various separation distances. 
The individual bubbles were formed and positioned by powering selected microheaters in 
a heater array. A series of bubble coalescence interactions then took place as the 
individual bubbles grew large enough to touch one another. 



•«». 



125 

A typical ebullition cycle which includes the coalescence of two bubbles is 
characterized by the following stages: nucleation and growth of two single bubbles, 
coalescence of dual bubbles, relatively long continued slow growth of the coalesced 
bubble, and finally departure of the coalesced bubble. There are also possibilities that the 
coalesced bubble would depart immediately or stay for a short growth period before 
departure. 

We have found that in general the coalescence enhances heat transfer as a result 
of creating rewetting of the heater surface by colder liquid and turbulent mixing effects. 
The enhancement is proportional to the ebullition cycle frequency and heater superheat. It 
was also predicted that the longer the heater separation distance is the higher the heat 
transfer rates would be enhanced. 

For the multibubble coalescence study, the key discovery is that the ultimate 
bubble that departs the heater surface is the product of a sequence of coalescences by 
dual bubbles. For heat transfer enhancement, it was determined that the time and space 
averaged heat flux for a given set of heaters increases with the number of bubbles 
involved and also with the separation distances among the heaters. In particular, we 
found that the heat flux levels for the internal heaters are relatively lower. 

O " 



CHAPTER 7 
MECHANISTIC MODEL FOR BUBBLE DEPARTURE AND BUBBLE 

COALESCENCE 

As presented in previous chapters, both the bubble departure/nucleation and 
coalescence result in heat flux spikes as shown in figure 7.1. These spikes were found to 
be the major contributions to heat transfer enhancement. Therefore, it is important to 
further our understanding of the heat transfer process by building mechanistic models. 
Following the flow visualization and physical understanding, the models developed in 



130 
120 

110 
■^100 
I 90 
^80 

W 60 
o 

X 50 

40 
30 
20 



Heat flux for heater #1 1 when #1 1 and #1 3 both at 1 00°C 
, Bubble departure 

Bubble coalescence 



U^MH^*^ 




'V/MwWA' 




. I 



2.5 



seconds 



3.5 



Figure 7.1 Typical heat flux spikes during bubble coalescence. 

this section are based on the transient process of rewetting heat transfer between the 
heater surface and colder liquid. The physical process is further explained in figure 7.2 
and figure 7.3 for the departure and coalescence, respectively. In figure 7.2(a), we see a 
sessile bubble during slow growth. When the buoyancy force is ready to lift the bubble as 



126 



127 

shown in figure 7.2(b), the necking process starts, which causes the liquid to initiate the 
downward motion. In figure 7.2(c), the bubble lifts off and accelerates upward which also 
gives the colder fluid more momentum to rush down to rewet the heater surface. For the 
coalescence as shown in figure 7.3, the coalesced bubble tends to be a vertical oval that 
results in re wetting of most of the surface area of the two heaters #1 and #13. 



Bubble before detachment 



bubble after detachment 



departing bubble 





liquid flow 




liquid flow 



(b) 



(c) 



Figure 7.2 The fluid flow induced by the bubble departure. 



7.1 Re wetting Model 

Based on the physical illustration given above, the rewetting model adopts the 
following assumptions: 

(1) The colder fluid with a temperature of Too covers the previously dry surface 
instantaneously at r = 0. . . ..., ... 

(2) The fluid at Too is a semi-infinite medium which is suddenly exposed to a 
constant interface temperature of T^ which corresponds to the heater temperature. 

(3) An effective conductivity K^jf is used to account for the convection and 
turbulent mixing effects. 



128 




Bubble outer profile , 



Contact line 



IT" 




rt^ 



(a) 





(b) 

Figure 7.3 The fluid flow induced by the bubble coalescence, (a) The model for heaters 
#1 and #13 completely wetted after coalescence, (b) The fluid flow induced by the bubble 

coalescence. 



For the semi-infmite solid transient conduction, Equation (5.58) given in 
Incropera and DeWitt (1996) is used and it is repeated here as follows 






(7.1) 



7.2 Results from the Re wetting Model 

The results from the re wetting model for two heater temperatures (100°C and 
110°C) have been shown in figure 7.4 and figure 7.5, where figure 7.4 is for bubble 
coalescence and figure 7.5 is for the departure process. In both figures 7.4(a) and 7.5(a), a 



129 



smaller plot is inserted to show relatively where the modeled portion is located in the 
entire ebullition cycle. From these figures, we can see that the predicted heat flux levels 
from the rewetting model agree well with the measured values. As the rewetting model is 
only valid for the heat flux spikes, it is therefore not adequate for the bubble slow growth 
periods that follow the departure and coalescence. 

Table 7.1 provides a list of the actual thermal conductivities and effective thermal 
conductivities. The ratio of the effective thermal conductivity to actual thermal 
conductivity is given in parentheses. It is clear that the effective thermal conductivity that 
accounts for the convection and turbulence is not sensitive to whether it is bubble 
departure or coalescence (3.5 vs. 3.63 at 100°C and 2.31 vs. 2.49 at 110°C) because the 
rewetting processes are similar for both cases. Whereas for different heater temperatures, 
the change of the effective thermal conductivity is quite substantial (2.31 vs. 3.5 for 
coalescence and 2.49 vs. 3.63 for departure). The reason is that both the departure and 
coalescence depend on the thermal properties and the surface tension that vary with the 
temperature. 
Table 7.1 Effective thermal conductivity (w/m-K) used in the rewetting model 





100°C 


110°C 


Actual thermal conductivity 


0.052 


0.051 


Effective thermal conductivity (departure) 


0.182(3.5) 


0.118 (2.31) 


Effective thermal conductivity (coalescence) 


0.189(3.63) 


0.127(2.49) 



130 




95 


r Model result for coalescence process (1 00°C) 


90 


'^N - 


85 
80 


: \ 


^ ^> / \ ■« *"• ^ Kfl«*nM>>iu«^ ^nAsK 


\^\ / \ 9 w IVieaSUrcQ Uala 


^sjt \ T ncwening niUQei 


.-75 
O 70 

M 60 

S 55 

X 
50 

45 

40 


I 130 
T 120 

: no 

— ^^°° 

' 1 90 

-in 

: §60 

- I 50 

I 30 


J bubble coalescer>ce 


35 


- ^ i 3 1 ia 
Moonds 


30 




( 


3 0.001 0.002 0.003 0.004 

Time (second) 

■>■ ■ ■ 


(a) 


80 


Model result for coalescence process (1 1 0°C) 


75 


- ^^^ 


70 


- 


^ ^-- ^ ■! <kM MI ■••» (J ^••*a 


\^ >|k • Measurea aai3 


^v \ ▼ rfcWcuing mOucI 


^ 65 

3 55 

g 50 

X 
45 


t "V^ 


40 


- ^--v 


35 


- 


30 






0.001 0.002 0.003 0.004 

Time (second) 


(b) 


Figure 7.4 The results from the rewetting model for the bubble coalescence, (a) Heaters at 

100°C;(b) Heaters at 11 0°C. 



131 



100 



90 



^^80 

E 
u 

5,70 

X 

3 

"Z 60 

(0 

X 
50 



40 - 



30 - 



Model results for departing process (1 00°) 




Experimental results 
Re wetting model 



*^^**^^^CIY*''^ 



-J I I I I I \ I I I I I I I I I L. 



0.002 0.004 0.006 

Time (seconds) 



_L 



0.008 



(a) 



100 



90 



-^80 

E 
o 

S.70 

X 

_3 

"Z 60 

(0 

« 

X 
50 



40 - 



30 - 



Model results for departing process (110°) 




Experimental results 
Rewetting model 



^^^^•^•^•^•v^* 






-I— I I I I I I I \ I I L. 



0.002 0.004 0.006 0.008 0.01 

Time (seconds) 



(b) 



Figure 7.5 The results from the rewetting model for the bubble departure, (a) Heaters at 

100°C; (b) Heaters at 11 0°C. 






CHAPTERS 
CONCLUSIONS AND FUTURE WORK 

8.1 Summary and Conclusions 

A heater array consisting of 96 microheaters was used in this research. Each 
heater on the array can be selected and individually controlled and maintained at constant 
temperature by the electronics feedback system. By generating a single bubble on a 
microheater at different temperatures, an experimental study of miniature-scale pool 
boiling heat transfer has been performed to provide a fundamental understanding on the 
heater size effect. The heat transfer history during the lifetime of a single bubble, which 
includes nucleation, growth, detachment and departure, has been measured at different 
heater temperatures. A major discovery is that for the heater size used in the current 
study, the boiling curve is composed of two regimes which are separated by a peak heat 
flux. In the lower superheat regime, the boiling is dominated by liquid rewetting and 
microlayer evaporation. While in the higher superheat regime, conduction through the 
vapor film and micro-convection play the key heat transfer role as the heater is covered 
by vapor all the time. In general, as the heater size decreases, the boiling curve moves 
towards higher heat fluxes with corresponding higher superheats. At a low AT, boiling is 
controlled by the microlayer evaporation and at a high AT, conduction dominates the heat 
transfer. We also observed that the bubble departure frequency increases with the 
superheat, but the departure size changes only very slightly. 

By selecting two or multiple heaters bubble coalescence experiments were 
performed to investigate the bubble coalescence phenomenon and its effect on boiling 

132 



133 

heat transfer. For bubble coalescence experiments, the individual bubbles were formed 
and positioned by powering selected microheaters in a heater array. A series of bubble 
coalescence interactions then took place, as the individual bubbles grew large enough to 
touch one another. A typical ebullition cycle which includes the coalescence of two 
bubbles is characterized by the following stages: nucleation and growth of two single 
bubbles, coalescence of dual bubbles, relatively long continued slow growth of the 
coalesced bubble, and finally departure of the coalesced bubble. There are also 
possibilities that the coalesced bubble would depart immediately or stay for a short 
growth period before departure. We have found that in general the coalescence enhances 
heat transfer as a result of creating rewetting of the heater surface by colder liquid and 
turbulent mixing effects. The enhancement is proportional to the ebullition cycle 
frequency and heater superheat. It was also predicted that the longer the heater separation 
distance is the higher the heat transfer rates would be from the heaters. For the 
multibubble coalescence study, the key discovery is that the ultimate bubble that departs 
the heater surface is the product of a sequence of coalescence by dual bubbles. For the 
heat transfer enhancement, it was determined that the time and space averaged heat flux 
for a given set of heaters increases with the number of bubbles involved and also with the 
separation distances among the heaters. In particular, we found that the heat flux levels 
for the internal heaters are relatively lower. 

f 8.2 Future Work 

Since boiling is a highly complicated heat transfer mode, its research is far from 
complete. The suggested future work following this research are listed in the following. 

1. Use the constant heat flux heater instead of a constant temperature heater. 



134 

2. Incline the heater surface at different orientations to study bubble coalescence 
effects. 

3. Perform a more detailed study on the microlayer and macrolayer of bubbles 
during growth period using optical methods. 

4. Investigate the subcooling effects on boiling heat transfer and on bubble 
coalescence. 

5. Study the bubble formation mechanism on a microheater when the heater is 
subjected to different heating rates. 



'^^'i'^iS 



i.:.. . . ,..:..,.- 



*■ i '^ "* 



APPENDIX A 
NOTES OF PROGRAMMING CODES FOR DATA ACQUISITION 

A.l Friendly Interface to Select Heaters - frmMain.frm 

The interface with 96 heaters in the array on which heaters can be selected 
according to experiment requirements has been utilized to facilitate the heaters selection. 
The form is shown in figure A.l. In this form, the following functions are to be realized: 

1. Initiate the D/A board (board 0) to output signals and the two A/D boards 
(board 1 and board 2) for data acquisition. The installation and configuration of the 
computerboards are accomplished. 

* 




iUHeateisAiiay HHE 


1 




' ■ 


— 












'■'■'■ 1 


7QQ : Zeio Heaters : 


















'.'.'.'.'. Setyp : 


















: : : : : Stat : 


































: : : : : stop : : 


















: : : : : Exit 


































'.'.'.'.'. Animate 




















































Labell 

, ; : : : Labec 
: : : : Labeia 

'■'■'■■ LabeW 


Selected Healers: : 


■ Select ON/Off;.r 










: 




















1 1 ^* 

r- 


ect/Set Temperature: 








1 










Fi^ 

2. Select heater 
number of selected heat 


;ur 

s. 
ers 


M 
a 


a; 
re 


n 

dn- 

St( 


'he 

mm 
jred 


mai 

8 
in 


n 

h 
P 


interfa 

eaters 
ablic V 

135 


ce to select heat 

can be selectee 
ariables that car 


ers. 

1. The heater code and 
I be used by other forms 



136 

and procedures. HeatersInfo.Heater(i) is the different heaters selected, and 
HeatersInfo.Num is the total number of heaters selected. 

3. Zero heaters. Set all digital pots to zero before turn on the 24 V power supply 
to the control circuits. . ^ - K , 

Also in this form, the technology of WindowsAPI was used to obtain the screen 
color of the mouse pointer. " " — - - 

Code A-1 

Private Declare Function GetPixel& Lib "gdi32" (ByVal hdc As Long, ByVal X As Long, ByVal 

Y As Long) 

Private Declare Function GetDC Lib "user32" (ByVal hwnd As Long) As Long 

Private Declare Function GetCursorPos Lib "user32" (IpPoint As POINT API) As Long 

Private Type POINTAPI 

X As Long 

Y As Long 
End Type 

Code A-2 

Private Sub form_MouseMove(Button As Integer, Shift As Integer, X As Single, Y As Single) 

Dim dsDC As Long 

Dim screenColour As Long 

Dim cp As POINTAPI 

'check the screen size 

'get desktop device context- to copy from 

GetCursorPos cp 

dsDC = GetDC(0&) 

screenColour = GetPixel(dsDC, cp.X, cp.Y) 

Label2.Caption = cp.X 

Labels. Caption = cp.Y 

'Note: the position is cp.X and cp.Y, which are the absolute coordinates on the screen. But the 

return 'values X, Y of _MouseMove are relative position values of the 

current form. 

If screenColour <> 65280 Then 

Lblcolor (previousColor).Caption = screenColour 
End If 
End Sub 

The selected heaters on the array have been programmed to exhibit the 
temperature corresponding to that set in the form frmAnimate.form. 



137 

A.2 Set the Temperature for Selected Heaters - (frmAnimate.frm) 

Multiple document interface (MDI) was used to individually set the heater 
temperature. Initial consideration was that we set the selected heaters temperature at the 
same time by setting the Dq values. In this experiment, we always set the heaters at the 
same temperature. For different heaters at the same temperature, Dq values are different. 
Therefore, the best way is to set the heaters temperature individually. From the 
frmMain.frm form, heaters were selected. In this form shown in figure A.2, we 
dynamically build the menu for all selected heaters that is under the menu: "Heaters". 
The code is given as follows. 



Code A- 3 

Private Sub Addltems() 

To show which heaters are selected. 

Dim i As Integer 

For i = 1 To HeatersInfo.Num 

Load mnultems(i) '**Dynamic adding items of the menu. 
mnuItems(i).Caption = "#" + Str(HeatersInfo.Heater(i) + 1) 
Nexti 
End Sub 



ii.Animate-[1-Heater 4] 



E3 . Exit 
Lab 



^ 



Window 



«4 
«1 
tt9 
«11 



iter 4 28 



Label4 



Setup i Download | Zero All I 



mE^ 



JffJxJ 



LabeB 



1\ 



Figure A.2 Heaters temperature form. 



138 

Special notes are that we need to add an dummy submenu to load the menus 
dynamically, as in this case mnultem with index as 0, which is a separation bar. Thus the 
index starts with the menu is actually 1. With the click the each other under menu of 
"Heaters", the child form corresponding to the heater is opened. Note that variable 
"Mark(i)" is used to mark whether the child form corresponding to the heater is opened 
or not to avoid to be opened twice. 



Code A-4 

Private Sub mnultems_click(index As Integer) 
Dim i As Integer 
If Mark(index) = False Then 
Dim frmDumm As New frmTemplate 
frmDumm.Show 

frmDumm.Caption = Str(index) + "-Heater " + Str(HeatersInfo.Heater(index) + 1) 
'Note: I put index in front of the Caption, so that we can index the children forms 
'when we unload them, in frmTemplate. 
Mark(index) = True 

For i = To 7 'set a mark for ActiveForm 
If i = index Then 

ActiveMark(i) = True 
Else 

ActiveMark(i) = False 
End If 
Next i 
' Labels. Caption = index 
End If 
End Sub 



The major function of this form is to set the heater temperature individually in its 
child form. Each child form corresponds to a horizontal scroll bar: hscDqValue(i). Only 
the hscDq Value that corresponds to the active child form is set visible. In this way, the 
scroll bar can be used to set the heater temperature of the active child form. The control 
Timer used in this form is used to detect the active child form and set the corresponding 
scroll bar. This use is not very efficient because use of Timer always slows the program 



139 

down, thus decrease the speed of data acquisition. The Child Form caption was used to 
distinguish them by adding the index number, as shown in the following. 



Code A- 5 

Private Sub mnultems_click(index As Integer) 
Dim i As Integer 
If Mark(index) = False Then 
Dim frmDumm As New frmTemplate 
frmDumm.Show 

frmDumm.Caption = Str(index) + "-Heater " + Str(HeatersInfo.Heater(index) + 1) 
'Note: I put index in front of the Caption, so that we can index the children forms 
'when we unload them, in frmTemplate. 



End Sub 

Private Sub Timerl_Timer() 

'This is used to detect which is Me.ActiveForm, so that it can be menu 
Dim i, j As Integer 

For i = To 7 'To obtain the index of the ActiveForm. 
If Mark(i) = True Then 

j = Val(Left$(frmAnimate.ActiveForm.Caption, 2)) 
End If 
Next I 



End Sub 

A.3 Programming the Digital Potentiometer 

The kernel of programming the temperature control is included in this form code. 
This kernel includes control of the circuit and inputting the Dq values to the circuit to set 
the digital potentiometer: DS 1267- 10. Its value ranges from to 10k ohms. It contains 
two wipers, each of them has 8 bits to be set, thus 2x2^=512 positions (from to 511). 
Note there is extra bit bO that is used distinguish which wiper is being set. 
Communication and control of DS1267 is accomplished through a 3-wire serial port 
interface that drives an internal control logic unit. The 3-wire serial interface consists of 
the three input signal: RST, CLK, and Dq. The RST control signal is used to enable the 3- 



140 

wire serial port operation of the device. It is an active high input and is required to begin 
any communication to the DS1267. The CLK signal input is used to provide timing 
synchronization for data input and output. The DQ signal line is used to transmit 
potentiometer wiper settings and the stack select bit configuration bO to the 17-bit I/O 
shift register of the DS 1267. 



Code A-6 

Sub SetPotValue(ByVal dq) 
Dimdqbit(17)AsByte \ 

' ■ t 

'The variable dqbit(17) is used to hold the converted dq values, which dqbit(O) is for bO 
for stack select. 

ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 34, 1) 'set reset high 'RST 
signal is set high. 

If ulStatoO Then Stop 

Fori = OTo 16 

ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 33, dqbit(i)) 'set dq 
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 32, 1) ' set clock 
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 33, 0) ' set clock 
ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 32, 0) ' set clock 

Next i 

ulStat% = cbDBitOut(DACBoardNum, FIRSTPORTA, 34, 0) ' set reset low 

End Sub 



A.4 Individual Heater Control 

The architecture of the system for the control of the circuits on the feedback cards 
is shown in the figure A.3. The multiplexers were used to realize the signal decoding. 
One multiplexer (MC74HC138A) is on the mother card. It is a one of eight decoder or 
demultiplexer. It decodes a three-bit Address to one-of-eight active-low outputs. The 8 
outputs are respectively sent to each card so that only one card accepts the high signal. 
(In this system there are only 6 cards, thus only 6 signals are used.) The other multiplexer 



141 

(MC74HC4514) is used to select the circuit on the card. The signal to each card is 
connected to the Chip select pin to enable the multiplexer on the card, while the other 
mulitiplexers on other cards are not enabled. The selected heater is converted to a 7-bit 
signal. The first 3 bits are output to the 74HC138A to select the card, the last 4 bits are 
output to the 74HC4514 to select the circuits. The following two lines are used to address 
the selected heater. 



i 



B 



Architecture for Addressing Heaters 



Computer 



Heater 
Number 



-Channel 
Number '^°"*'^'^'°"'°^'"^t 



.Card Conversion to blnai ^/ 

Numbe 



Software 



D/A 
computer- 
board 



channel select 



Multiplex 



( ard Select 





Multiplex 


Channel 












^, . * 


































ch select 















Channel D- 15 

nnnn 

DDDD 

nnnn 
nnnn 



ICanj Select 



J 



nnnn 
nnnn 
nnnn 
nnnn 



Card -6 



Mono Fluidics and Heat Transfer Lab 
University of Florida 
Gainesville FL32611 
Prepared By Tailian 






B 



A 



Figure A.3 The architecture for addressing the selected heaters. 



142 



Code A-7 

Addr = CircuitSelect(SelHeater) 

ulStat = cbDOut(DACBoardNum, SECONDPORTA, Addr) 



Data acquisition is simply accomplished by using the computerboards library 
function "cbAIn", which is shown as follows. 



Code A-8 

Function GetHeaterVoltage(PortNum, CardNum) 

Dim voltage 

ulStat% = cbAIn(CardNum, PortNum, UNIIOVOLTS, voltage) 
'value must be defined. 

voltage = voltage * 10 / 4096 

GetHeaterVoltage = voltage 
End Function 



For data acquisition, an important thing is that the pins on the A/D cards are not 
consistent with the heater numbers (from to 95). Therefore a function is required to 
convert this inconsistency, which is done by "DAS48PortNum". The figure A.4 is used to 
illustrate this inconsistency. 



Code A-9 

Function DAS48PortNum(Heater) As Integer 
Dim PortNum As Integer 
If Heater Mod 2= 1 Then 
PortNum = (Heater - 1 ) / 2 
PortNum = PortNum + 24 
Else 

PortNum = Heater / 2 "1 "* 

End If 

DAS48PortNum = PortNum 
End Function 



t.'-s 



143 



View Kroin Cornponenl Side of lioard 



UGNO 

CH4TH/CH23LOW 

CHM HI I CM 22 LOW 

CH4SHI/CH21LOW 

CH 44 H) ( CH 20 LOW 

CH 43 HI f CH 19 LOW 

CH42M/CHIS10W 

CH4UfllCH tJLOW 

CH40H)/CHt6lOW 

CH3«HWCHISI.0W 

CHMH1(CMI410W 

CH37HlfCH 13 LOW 

CH3eHllCHI2LOW 

CM3SHICHM10W 

CH34HIICMI0LCIW 

CH 33 Hi 'CHI LOW 

CH32Hi(CMIlOW 

CHSrHI/CH/LOW 

CH»Mi;CH6L0W 

CM2»MUCH5LOW 

CH7«HlrCH4LOW 

CH2!HI/CH3tOW 

CH2(HIICH2lOW 

CH25Ht/CM1LOW 

CH24HIICHOI.OW 



IIGND 
CM HI 23 
CM Ml 22 
CH MI21 
CH Ml 20 




Channel 
Number 



Pin 
Number 



Figure A.4 The pins layout of the D/A cards. 

A.5 Data Acquisition - (frmADConv.frm) 

The major function of this form shown in figure A.5 is data acquisition in which 
the acquisition time and output file can be selected. The heater temperature needs to be 
set before starting the acquisition. The main feature used in this form is the use of SQL. 
The database that is built using "Visual Data Manager" contains the information of each 
heater including heater area, heater resistance values. These data are accessed in this form 
after the voltage across the heater have been acquired, then used to calculate the heat flux 
dissipated by the heater. The control "data" is included in this form to realize the access 
by using SQL language. 

The following is the code to access the data stored in the database. 

Code A-10 



Datal.Recordset.Move SelectedHeater - Data 1. Recordset. AbsolutePosition 



144 



RMResist = Datal.Recordset.Fields("Resistance").Value 
realResist = RMResist / (1 - 0.002 * (HeatersInfo.Temperature - 25)) 
HeaterArea = Datal.Recordset.Fields(" Area"). Value 



Three combo controls have been implemented in this form. One is the control 
"cmbSelect" which is used to contain the heaters selected in the Main Form. By selecting 
one of them, the heater can be accessed for data acquisition. The control "cmbDuration" 
is used to choose the time for data acquisition. The control "cmbTemp" is used to select 
the temperature that the heater is set, which has to be same as the actual temperature the 
heater is set. 






K* 



f'4 n 



vC^rop - 



1 in. Data Acquiie - Compuleiboafds 


■^^.Inlxi 










Start at 3:20:50 PM 
Finish at 3:20:54 PM 
Ac Time Period: 4.00781 3 
D. P. Acquired: 13144 




Selected Heaters: 


- 


S elect A/DTime(s): 
4 2\ 




^Download Completed! 








1 

Output Re: Browse 




\ Start 






C: \customAD \D ataFiles\test. dat 

1 


Stop 


1 npulH eater Temperatue: 95 ▼ 


Exit 









Figure A.5 The data acquisition form. 



A.6 Child Form Template - (frmTempIate.frm) 

This form is built to set up the template child form so that each child form has the 
same format. In this form, the unloading of the ActiveForm of the child forms is detected 



145 

by checking the index associated with the form caption, which is shown in the following 
code. After this unloading, the Timer control in frmAnimate.frm automatically detects 
the current ActiveForm. .- 



Code A- 11 

Private Sub Form_unLoad(index As Integer) 

'The whole idea is to reopen the child form after it is open and closed, 
by using the using index in front of the Caption. 
Dim strlndex As String 
Dim sstrlndex As Integer 

'frmAnimate.Labell. Caption = Me.Caption 
strlndex = Left$(Me. Caption, 2) 
'For some reason, if Left$(me.caption, 1) is used, the result is blank. 
' frmAnimate.Label2.Caption = strlndex 
sstrlndex = Val(strlndex) 
Mark(sstrlndex) = False 
End Sub 



Actually, Timer control does not have to be always enabled since its sole function 
is to detect the current ActiveForm. Here, we can modify the code so that only when 
there is a change of ActiveForm, the Timer is enabled. 

In addition to the Forms described above, this software also includes the 
following modules: DataStructure.bas, ModDAC.bas, ModADC.bas, Heatersinfo.bas, 
Cbw.bas, PubConst.bas, PubVariables.bas. Among these, Cbw.bas is the module 
included to enable the computerboards functions. 






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281-296. 



BIOGRAPHICAL SKETCH 

Tailian Chen received his bachelor's degree in mechanical engineering in 1990, 
and continued his study in automotive engineering. He finished his Master of Science 
degree in 1993 at Jiangsu University of Science and Technology in Zhenjiang, China. 
After that, he joined Panda Motors (China) Corporation to be an electro-mechanical 
engineer until December 1998. During his tenure in PMCC his responsibilities included 
technical, engineering work and project management. 

In January 1999, he moved to Gainesville, Florida, USA, to pursue his Ph.D 
degree in mechanical engineering. His research is on microscale boiling heat transfer. His 
archival publications have appeared in the International Journal of Heat and Mass 
Transfer. 






H 



/. 
*^.'' 



*6^ 






150 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



Jiii/^i> A/. (vlyuiA.'^ 



Jacob N. Chung, Chair 

Professor of Mechanical Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



'^h^yj 





F. Klausner 
bssor of Mechanical Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




William E. Lear, Jr. 
Associate Professor of Mechanical 
Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 





'huomin Zhang 
Associate Professor of Mechanical 
Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 



Vi.n.Vuvtw^C^ 



Ulrich H. Kurzweg 
Professor of Aerospace Engineering, 
Mechanics and Engineering Science 



This dissertation was submitted to the Graduate Faculty of the College of 
Engineering and to the Graduate School and was accepted as partial fulfillment of the 
requirements for the degree of Doctor of Philosophy. 



August 2002 



/ 



Pramod P. Khargonekar 
Dean, College of Engineering 



Winfred M. Phillips 
Dean, Graduate School 






J^." 




,C5I3^ 



UNIVERSITY OF FLORIDA 



-sr- ' .' 



3 1262 08555 3567 



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